Numerical method MATLAB code
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I am unable to get plot of following code of numerical methods. Plot command throw error of not same vector length
% Title: Comparison of Trapezoid and Simpson's Composite Methods for T-distribution and Normal Distribution
% Name: TXXXX XXXXXXX
% Class: Scientific Computing
% Define the probability density functions for T-distribution and normal distribution
f_t = @(x, v) gamma((v+1)/2) / (sqrt(v*pi) * gamma(v/2)) * (1 + x.^2/v).^(-(v+1)/2);
f_norm = @(x) exp(-x.^2/2) / sqrt(2*pi);
% Define the integration interval and the number of subintervals for approximation
a = -5;
b = 5;
n = 1000;
% Use trapezoid method to approximate the integrals
h = (b-a)/n;
x = linspace(a, b, n+1);
t_trap = h/2 * (f_t(x(1:end-1), 10) + f_t(x(2:end), 10));
norm_trap = h/2 * (f_norm(x(1:end-1)) + f_norm(x(2:end)));
% Use Simpson's composite method to approximate the integrals
x = linspace(a, b, 2*n+1);
h = (b-a)/(2*n);
t_simp = h/3 * (f_t(x(1:2:end-2), 10) + 4*f_t(x(2:2:end-1), 10) + f_t(x(3:2:end), 10));
norm_simp = h/3 * (f_norm(x(1:2:end-2)) + 4*f_norm(x(2:2:end-1)) + f_norm(x(3:2:end)));
% Calculate the exact values of the integrals
t_exact = integral(@(x) f_t(x, 10), -Inf, Inf);
norm_exact = integral(@(x) f_norm(x), -Inf, Inf);
% Compare the approximations with the exact values
fprintf('T-distribution integral:\n');
fprintf('Trapezoid method: %f\n', t_trap);
fprintf('Simpson''s composite method: %f\n', t_simp);
fprintf('Exact value: %f\n', t_exact);
fprintf('\nNormal distribution integral:\n');
fprintf('Trapezoid method: %f\n', norm_trap);
fprintf('Simpson''s composite method: %f\n', norm_simp);
fprintf('Exact value: %f\n', norm_exact);
% Plot the approximations and the exact values
figure;
subplot(2,1,1);
plot(x, f_t(x, 10), 'k', x(1:end-1), t_trap, 'r', x(1:2:end), t_simp, 'b--');
legend('Exact', 'Trapezoid', 'Simpson''s');
title('T-distribution Probability Density Function');
subplot(2,1,2);
plot(x, f_norm(x), 'k', x(1:end-1), norm_trap, 'r', x(1:2:end), norm_simp, 'b--');
legend('Exact', 'Trapezoid', 'Simpson''s');
title('Normal Distribution Probability Density Function');
7 个评论
Torsten
2023-4-6
t_trap, norm_trap, t_simp and norm_simp are vectors that are approximations of integrals over certain subintervals of [a,b], namely over two or three subsequent grid points. What's the sense of it ?
Torsten
2023-4-6
What do you want to plot ? The integral is a single value and x is a vector of grid points. Or did you try to compute the integrals starting from "a" and ending in the different x-values up to x=b ?
Shoaib Salim
2023-4-6
In plot command i get error of different vector length. How can i change it to get plot similar to exact value of 1
Torsten
2023-4-7
编辑:Torsten
2023-4-7
Didn't you understand what I mean ?
What do you want to plot in case you determine the value of an integral over a predefined interval ?
The only thing I can think of is to plot integral_{t=a}^{t=x} f(t) dt in a given grid point x. But you don't calculate these integrals in your code and you didn't comment on this suggestion I've already done earlier.
采纳的回答
Oguz Kaan Hancioglu
2023-4-6
The length(x(1:end-1)) and length(t_trap) are not equal. Also, the length(x(1:2:end)) and length(t_simp) are not the equal. I think you can equal the length(x(1:2:end)) and length(t_simp) by changing x(3:2:end). However, the length(x(1:end-1)) is equal twice of length(t_trap).
% Title: Comparison of Trapezoid and Simpson's Composite Methods for T-distribution and Normal Distribution
% Name: TXXXX XXXXXXX
% Class: Scientific Computing
% Define the probability density functions for T-distribution and normal distribution
f_t = @(x, v) gamma((v+1)/2) / (sqrt(v*pi) * gamma(v/2)) * (1 + x.^2/v).^(-(v+1)/2);
f_norm = @(x) exp(-x.^2/2) / sqrt(2*pi);
% Define the integration interval and the number of subintervals for approximation
a = -5;
b = 5;
n = 1000;
% Use trapezoid method to approximate the integrals
h = (b-a)/n;
x = linspace(a, b, n+1);
t_trap = h/2 * (f_t(x(1:end-1), 10) + f_t(x(2:end), 10));
norm_trap = h/2 * (f_norm(x(1:end-1)) + f_norm(x(2:end)));
% Use Simpson's composite method to approximate the integrals
x = linspace(a, b, 2*n+1);
h = (b-a)/(2*n);
t_simp = h/3 * (f_t(x(1:2:end-2), 10) + 4*f_t(x(2:2:end-1), 10) + f_t(x(3:2:end), 10));
norm_simp = h/3 * (f_norm(x(1:2:end-2)) + 4*f_norm(x(2:2:end-1)) + f_norm(x(3:2:end)));
% Calculate the exact values of the integrals
t_exact = integral(@(x) f_t(x, 10), -Inf, Inf);
norm_exact = integral(@(x) f_norm(x), -Inf, Inf);
% Compare the approximations with the exact values
fprintf('T-distribution integral:\n');
T-distribution integral:
fprintf('Trapezoid method: %f\n', t_trap);
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000009
Trapezoid method: 0.000009
Trapezoid method: 0.000009
Trapezoid method: 0.000009
Trapezoid method: 0.000009
Trapezoid method: 0.000009
Trapezoid method: 0.000010
Trapezoid method: 0.000010
Trapezoid method: 0.000010
Trapezoid method: 0.000010
Trapezoid method: 0.000010
Trapezoid method: 0.000010
Trapezoid method: 0.000010
Trapezoid method: 0.000011
Trapezoid method: 0.000011
Trapezoid method: 0.000011
Trapezoid method: 0.000011
Trapezoid method: 0.000011
Trapezoid method: 0.000012
Trapezoid method: 0.000012
Trapezoid method: 0.000012
Trapezoid method: 0.000012
Trapezoid method: 0.000012
Trapezoid method: 0.000013
Trapezoid method: 0.000013
Trapezoid method: 0.000013
Trapezoid method: 0.000013
Trapezoid method: 0.000013
Trapezoid method: 0.000014
Trapezoid method: 0.000014
Trapezoid method: 0.000014
Trapezoid method: 0.000014
Trapezoid method: 0.000015
Trapezoid method: 0.000015
Trapezoid method: 0.000015
Trapezoid method: 0.000015
Trapezoid method: 0.000016
Trapezoid method: 0.000016
Trapezoid method: 0.000016
Trapezoid method: 0.000016
Trapezoid method: 0.000017
Trapezoid method: 0.000017
Trapezoid method: 0.000017
Trapezoid method: 0.000018
Trapezoid method: 0.000018
Trapezoid method: 0.000018
Trapezoid method: 0.000019
Trapezoid method: 0.000019
Trapezoid method: 0.000019
Trapezoid method: 0.000019
Trapezoid method: 0.000020
Trapezoid method: 0.000020
Trapezoid method: 0.000020
Trapezoid method: 0.000021
Trapezoid method: 0.000021
Trapezoid method: 0.000022
Trapezoid method: 0.000022
Trapezoid method: 0.000022
Trapezoid method: 0.000023
Trapezoid method: 0.000023
Trapezoid method: 0.000023
Trapezoid method: 0.000024
Trapezoid method: 0.000024
Trapezoid method: 0.000025
Trapezoid method: 0.000025
Trapezoid method: 0.000026
Trapezoid method: 0.000026
Trapezoid method: 0.000026
Trapezoid method: 0.000027
Trapezoid method: 0.000027
Trapezoid method: 0.000028
Trapezoid method: 0.000028
Trapezoid method: 0.000029
Trapezoid method: 0.000029
Trapezoid method: 0.000030
Trapezoid method: 0.000030
Trapezoid method: 0.000031
Trapezoid method: 0.000031
Trapezoid method: 0.000032
Trapezoid method: 0.000032
Trapezoid method: 0.000033
Trapezoid method: 0.000034
Trapezoid method: 0.000034
Trapezoid method: 0.000035
Trapezoid method: 0.000035
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Trapezoid method: 0.000037
Trapezoid method: 0.000037
Trapezoid method: 0.000038
Trapezoid method: 0.000039
Trapezoid method: 0.000039
Trapezoid method: 0.000040
Trapezoid method: 0.000041
Trapezoid method: 0.000041
Trapezoid method: 0.000042
Trapezoid method: 0.000043
Trapezoid method: 0.000043
Trapezoid method: 0.000044
Trapezoid method: 0.000045
Trapezoid method: 0.000046
Trapezoid method: 0.000047
Trapezoid method: 0.000047
Trapezoid method: 0.000048
Trapezoid method: 0.000049
Trapezoid method: 0.000050
Trapezoid method: 0.000051
Trapezoid method: 0.000052
Trapezoid method: 0.000053
Trapezoid method: 0.000054
Trapezoid method: 0.000054
Trapezoid method: 0.000055
Trapezoid method: 0.000056
Trapezoid method: 0.000057
Trapezoid method: 0.000058
Trapezoid method: 0.000059
Trapezoid method: 0.000060
Trapezoid method: 0.000062
Trapezoid method: 0.000063
Trapezoid method: 0.000064
Trapezoid method: 0.000065
Trapezoid method: 0.000066
Trapezoid method: 0.000067
Trapezoid method: 0.000068
Trapezoid method: 0.000069
Trapezoid method: 0.000071
Trapezoid method: 0.000072
Trapezoid method: 0.000073
Trapezoid method: 0.000074
Trapezoid method: 0.000076
Trapezoid method: 0.000077
Trapezoid method: 0.000078
Trapezoid method: 0.000080
Trapezoid method: 0.000081
Trapezoid method: 0.000083
Trapezoid method: 0.000084
Trapezoid method: 0.000086
Trapezoid method: 0.000087
Trapezoid method: 0.000089
Trapezoid method: 0.000090
Trapezoid method: 0.000092
Trapezoid method: 0.000093
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Trapezoid method: 0.000097
Trapezoid method: 0.000098
Trapezoid method: 0.000100
Trapezoid method: 0.000102
Trapezoid method: 0.000104
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Trapezoid method: 0.000107
Trapezoid method: 0.000109
Trapezoid method: 0.000111
Trapezoid method: 0.000113
Trapezoid method: 0.000115
Trapezoid method: 0.000117
Trapezoid method: 0.000119
Trapezoid method: 0.000121
Trapezoid method: 0.000123
Trapezoid method: 0.000125
Trapezoid method: 0.000128
Trapezoid method: 0.000130
Trapezoid method: 0.000132
Trapezoid method: 0.000134
Trapezoid method: 0.000137
Trapezoid method: 0.000139
Trapezoid method: 0.000142
Trapezoid method: 0.000144
Trapezoid method: 0.000147
Trapezoid method: 0.000149
Trapezoid method: 0.000152
Trapezoid method: 0.000154
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Trapezoid method: 0.000160
Trapezoid method: 0.000163
Trapezoid method: 0.000165
Trapezoid method: 0.000168
Trapezoid method: 0.000171
Trapezoid method: 0.000174
Trapezoid method: 0.000177
Trapezoid method: 0.000180
Trapezoid method: 0.000183
Trapezoid method: 0.000187
Trapezoid method: 0.000190
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Trapezoid method: 0.000200
Trapezoid method: 0.000203
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Trapezoid method: 0.000210
Trapezoid method: 0.000214
Trapezoid method: 0.000218
Trapezoid method: 0.000222
Trapezoid method: 0.000225
Trapezoid method: 0.000229
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Trapezoid method: 0.000237
Trapezoid method: 0.000241
Trapezoid method: 0.000245
Trapezoid method: 0.000250
Trapezoid method: 0.000254
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Trapezoid method: 0.000263
Trapezoid method: 0.000267
Trapezoid method: 0.000272
Trapezoid method: 0.000276
Trapezoid method: 0.000281
Trapezoid method: 0.000286
Trapezoid method: 0.000291
Trapezoid method: 0.000296
Trapezoid method: 0.000301
Trapezoid method: 0.000306
Trapezoid method: 0.000311
Trapezoid method: 0.000316
Trapezoid method: 0.000321
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Trapezoid method: 0.000332
Trapezoid method: 0.000338
Trapezoid method: 0.000344
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Trapezoid method: 0.000355
Trapezoid method: 0.000361
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Trapezoid method: 0.000380
Trapezoid method: 0.000386
Trapezoid method: 0.000392
Trapezoid method: 0.000399
Trapezoid method: 0.000406
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Trapezoid method: 0.000426
Trapezoid method: 0.000433
Trapezoid method: 0.000440
Trapezoid method: 0.000447
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Trapezoid method: 0.000462
Trapezoid method: 0.000470
Trapezoid method: 0.000477
Trapezoid method: 0.000485
Trapezoid method: 0.000493
Trapezoid method: 0.000501
Trapezoid method: 0.000509
Trapezoid method: 0.000518
Trapezoid method: 0.000526
Trapezoid method: 0.000534
Trapezoid method: 0.000543
Trapezoid method: 0.000552
Trapezoid method: 0.000561
Trapezoid method: 0.000570
Trapezoid method: 0.000579
Trapezoid method: 0.000588
Trapezoid method: 0.000597
Trapezoid method: 0.000607
Trapezoid method: 0.000616
Trapezoid method: 0.000626
Trapezoid method: 0.000636
Trapezoid method: 0.000646
Trapezoid method: 0.000656
Trapezoid method: 0.000666
Trapezoid method: 0.000677
Trapezoid method: 0.000687
Trapezoid method: 0.000698
Trapezoid method: 0.000709
Trapezoid method: 0.000720
Trapezoid method: 0.000731
Trapezoid method: 0.000742
Trapezoid method: 0.000754
Trapezoid method: 0.000765
Trapezoid method: 0.000777
Trapezoid method: 0.000789
Trapezoid method: 0.000801
Trapezoid method: 0.000813
Trapezoid method: 0.000825
Trapezoid method: 0.000837
Trapezoid method: 0.000850
Trapezoid method: 0.000863
Trapezoid method: 0.000876
Trapezoid method: 0.000889
Trapezoid method: 0.000902
Trapezoid method: 0.000915
Trapezoid method: 0.000929
Trapezoid method: 0.000942
Trapezoid method: 0.000956
Trapezoid method: 0.000970
Trapezoid method: 0.000984
Trapezoid method: 0.000999
Trapezoid method: 0.001013
Trapezoid method: 0.001028
Trapezoid method: 0.001042
Trapezoid method: 0.001057
Trapezoid method: 0.001072
Trapezoid method: 0.001088
Trapezoid method: 0.001103
Trapezoid method: 0.001119
Trapezoid method: 0.001134
Trapezoid method: 0.001150
Trapezoid method: 0.001166
Trapezoid method: 0.001182
Trapezoid method: 0.001199
Trapezoid method: 0.001215
Trapezoid method: 0.001232
Trapezoid method: 0.001249
Trapezoid method: 0.001266
Trapezoid method: 0.001283
Trapezoid method: 0.001300
Trapezoid method: 0.001318
Trapezoid method: 0.001336
Trapezoid method: 0.001353
Trapezoid method: 0.001371
Trapezoid method: 0.001389
Trapezoid method: 0.001408
Trapezoid method: 0.001426
Trapezoid method: 0.001445
Trapezoid method: 0.001463
Trapezoid method: 0.001482
Trapezoid method: 0.001501
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Trapezoid method: 0.001540
Trapezoid method: 0.001559
Trapezoid method: 0.001579
Trapezoid method: 0.001599
Trapezoid method: 0.001618
Trapezoid method: 0.001638
Trapezoid method: 0.001659
Trapezoid method: 0.001679
Trapezoid method: 0.001699
Trapezoid method: 0.001720
Trapezoid method: 0.001741
Trapezoid method: 0.001761
Trapezoid method: 0.001782
Trapezoid method: 0.001803
Trapezoid method: 0.001825
Trapezoid method: 0.001846
Trapezoid method: 0.001867
Trapezoid method: 0.001889
Trapezoid method: 0.001911
Trapezoid method: 0.001932
Trapezoid method: 0.001954
Trapezoid method: 0.001976
Trapezoid method: 0.001998
Trapezoid method: 0.002020
Trapezoid method: 0.002043
Trapezoid method: 0.002065
Trapezoid method: 0.002087
Trapezoid method: 0.002110
Trapezoid method: 0.002132
Trapezoid method: 0.002155
Trapezoid method: 0.002178
Trapezoid method: 0.002200
Trapezoid method: 0.002223
Trapezoid method: 0.002246
Trapezoid method: 0.002269
Trapezoid method: 0.002292
Trapezoid method: 0.002315
Trapezoid method: 0.002338
Trapezoid method: 0.002361
Trapezoid method: 0.002384
Trapezoid method: 0.002408
Trapezoid method: 0.002431
Trapezoid method: 0.002454
Trapezoid method: 0.002477
Trapezoid method: 0.002500
Trapezoid method: 0.002524
Trapezoid method: 0.002547
Trapezoid method: 0.002570
Trapezoid method: 0.002593
Trapezoid method: 0.002616
Trapezoid method: 0.002640
Trapezoid method: 0.002663
Trapezoid method: 0.002686
Trapezoid method: 0.002709
Trapezoid method: 0.002732
Trapezoid method: 0.002755
Trapezoid method: 0.002778
Trapezoid method: 0.002800
Trapezoid method: 0.002823
Trapezoid method: 0.002846
Trapezoid method: 0.002868
Trapezoid method: 0.002891
Trapezoid method: 0.002913
Trapezoid method: 0.002936
Trapezoid method: 0.002958
Trapezoid method: 0.002980
Trapezoid method: 0.003002
Trapezoid method: 0.003024
Trapezoid method: 0.003045
Trapezoid method: 0.003067
Trapezoid method: 0.003088
Trapezoid method: 0.003110
Trapezoid method: 0.003131
Trapezoid method: 0.003152
Trapezoid method: 0.003172
Trapezoid method: 0.003193
Trapezoid method: 0.003213
Trapezoid method: 0.003234
Trapezoid method: 0.003254
Trapezoid method: 0.003273
Trapezoid method: 0.003293
Trapezoid method: 0.003312
Trapezoid method: 0.003332
Trapezoid method: 0.003351
Trapezoid method: 0.003369
Trapezoid method: 0.003388
Trapezoid method: 0.003406
Trapezoid method: 0.003424
Trapezoid method: 0.003442
Trapezoid method: 0.003459
Trapezoid method: 0.003476
Trapezoid method: 0.003493
Trapezoid method: 0.003510
Trapezoid method: 0.003526
Trapezoid method: 0.003542
Trapezoid method: 0.003558
Trapezoid method: 0.003573
Trapezoid method: 0.003589
Trapezoid method: 0.003603
Trapezoid method: 0.003618
Trapezoid method: 0.003632
Trapezoid method: 0.003646
Trapezoid method: 0.003659
Trapezoid method: 0.003673
Trapezoid method: 0.003685
Trapezoid method: 0.003698
Trapezoid method: 0.003710
Trapezoid method: 0.003722
Trapezoid method: 0.003733
Trapezoid method: 0.003744
Trapezoid method: 0.003755
Trapezoid method: 0.003765
Trapezoid method: 0.003775
Trapezoid method: 0.003784
Trapezoid method: 0.003794
Trapezoid method: 0.003802
Trapezoid method: 0.003811
Trapezoid method: 0.003819
Trapezoid method: 0.003826
Trapezoid method: 0.003833
Trapezoid method: 0.003840
Trapezoid method: 0.003846
Trapezoid method: 0.003852
Trapezoid method: 0.003858
Trapezoid method: 0.003863
Trapezoid method: 0.003868
Trapezoid method: 0.003872
Trapezoid method: 0.003876
Trapezoid method: 0.003879
Trapezoid method: 0.003882
Trapezoid method: 0.003885
Trapezoid method: 0.003887
Trapezoid method: 0.003888
Trapezoid method: 0.003890
Trapezoid method: 0.003891
Trapezoid method: 0.003891
Trapezoid method: 0.003891
Trapezoid method: 0.003891
Trapezoid method: 0.003890
Trapezoid method: 0.003888
Trapezoid method: 0.003887
Trapezoid method: 0.003885
Trapezoid method: 0.003882
Trapezoid method: 0.003879
Trapezoid method: 0.003876
Trapezoid method: 0.003872
Trapezoid method: 0.003868
Trapezoid method: 0.003863
Trapezoid method: 0.003858
Trapezoid method: 0.003852
Trapezoid method: 0.003846
Trapezoid method: 0.003840
Trapezoid method: 0.003833
Trapezoid method: 0.003826
Trapezoid method: 0.003819
Trapezoid method: 0.003811
Trapezoid method: 0.003802
Trapezoid method: 0.003794
Trapezoid method: 0.003784
Trapezoid method: 0.003775
Trapezoid method: 0.003765
Trapezoid method: 0.003755
Trapezoid method: 0.003744
Trapezoid method: 0.003733
Trapezoid method: 0.003722
Trapezoid method: 0.003710
Trapezoid method: 0.003698
Trapezoid method: 0.003685
Trapezoid method: 0.003673
Trapezoid method: 0.003659
Trapezoid method: 0.003646
Trapezoid method: 0.003632
Trapezoid method: 0.003618
Trapezoid method: 0.003603
Trapezoid method: 0.003589
Trapezoid method: 0.003573
Trapezoid method: 0.003558
Trapezoid method: 0.003542
Trapezoid method: 0.003526
Trapezoid method: 0.003510
Trapezoid method: 0.003493
Trapezoid method: 0.003476
Trapezoid method: 0.003459
Trapezoid method: 0.003442
Trapezoid method: 0.003424
Trapezoid method: 0.003406
Trapezoid method: 0.003388
Trapezoid method: 0.003369
Trapezoid method: 0.003351
Trapezoid method: 0.003332
Trapezoid method: 0.003312
Trapezoid method: 0.003293
Trapezoid method: 0.003273
Trapezoid method: 0.003254
Trapezoid method: 0.003234
Trapezoid method: 0.003213
Trapezoid method: 0.003193
Trapezoid method: 0.003172
Trapezoid method: 0.003152
Trapezoid method: 0.003131
Trapezoid method: 0.003110
Trapezoid method: 0.003088
Trapezoid method: 0.003067
Trapezoid method: 0.003045
Trapezoid method: 0.003024
Trapezoid method: 0.003002
Trapezoid method: 0.002980
Trapezoid method: 0.002958
Trapezoid method: 0.002936
Trapezoid method: 0.002913
Trapezoid method: 0.002891
Trapezoid method: 0.002868
Trapezoid method: 0.002846
Trapezoid method: 0.002823
Trapezoid method: 0.002800
Trapezoid method: 0.002778
Trapezoid method: 0.002755
Trapezoid method: 0.002732
Trapezoid method: 0.002709
Trapezoid method: 0.002686
Trapezoid method: 0.002663
Trapezoid method: 0.002640
Trapezoid method: 0.002616
Trapezoid method: 0.002593
Trapezoid method: 0.002570
Trapezoid method: 0.002547
Trapezoid method: 0.002524
Trapezoid method: 0.002500
Trapezoid method: 0.002477
Trapezoid method: 0.002454
Trapezoid method: 0.002431
Trapezoid method: 0.002408
Trapezoid method: 0.002384
Trapezoid method: 0.002361
Trapezoid method: 0.002338
Trapezoid method: 0.002315
Trapezoid method: 0.002292
Trapezoid method: 0.002269
Trapezoid method: 0.002246
Trapezoid method: 0.002223
Trapezoid method: 0.002200
Trapezoid method: 0.002178
Trapezoid method: 0.002155
Trapezoid method: 0.002132
Trapezoid method: 0.002110
Trapezoid method: 0.002087
Trapezoid method: 0.002065
Trapezoid method: 0.002043
Trapezoid method: 0.002020
Trapezoid method: 0.001998
Trapezoid method: 0.001976
Trapezoid method: 0.001954
Trapezoid method: 0.001932
Trapezoid method: 0.001911
Trapezoid method: 0.001889
Trapezoid method: 0.001867
Trapezoid method: 0.001846
Trapezoid method: 0.001825
Trapezoid method: 0.001803
Trapezoid method: 0.001782
Trapezoid method: 0.001761
Trapezoid method: 0.001741
Trapezoid method: 0.001720
Trapezoid method: 0.001699
Trapezoid method: 0.001679
Trapezoid method: 0.001659
Trapezoid method: 0.001638
Trapezoid method: 0.001618
Trapezoid method: 0.001599
Trapezoid method: 0.001579
Trapezoid method: 0.001559
Trapezoid method: 0.001540
Trapezoid method: 0.001520
Trapezoid method: 0.001501
Trapezoid method: 0.001482
Trapezoid method: 0.001463
Trapezoid method: 0.001445
Trapezoid method: 0.001426
Trapezoid method: 0.001408
Trapezoid method: 0.001389
Trapezoid method: 0.001371
Trapezoid method: 0.001353
Trapezoid method: 0.001336
Trapezoid method: 0.001318
Trapezoid method: 0.001300
Trapezoid method: 0.001283
Trapezoid method: 0.001266
Trapezoid method: 0.001249
Trapezoid method: 0.001232
Trapezoid method: 0.001215
Trapezoid method: 0.001199
Trapezoid method: 0.001182
Trapezoid method: 0.001166
Trapezoid method: 0.001150
Trapezoid method: 0.001134
Trapezoid method: 0.001119
Trapezoid method: 0.001103
Trapezoid method: 0.001088
Trapezoid method: 0.001072
Trapezoid method: 0.001057
Trapezoid method: 0.001042
Trapezoid method: 0.001028
Trapezoid method: 0.001013
Trapezoid method: 0.000999
Trapezoid method: 0.000984
Trapezoid method: 0.000970
Trapezoid method: 0.000956
Trapezoid method: 0.000942
Trapezoid method: 0.000929
Trapezoid method: 0.000915
Trapezoid method: 0.000902
Trapezoid method: 0.000889
Trapezoid method: 0.000876
Trapezoid method: 0.000863
Trapezoid method: 0.000850
Trapezoid method: 0.000837
Trapezoid method: 0.000825
Trapezoid method: 0.000813
Trapezoid method: 0.000801
Trapezoid method: 0.000789
Trapezoid method: 0.000777
Trapezoid method: 0.000765
Trapezoid method: 0.000754
Trapezoid method: 0.000742
Trapezoid method: 0.000731
Trapezoid method: 0.000720
Trapezoid method: 0.000709
Trapezoid method: 0.000698
Trapezoid method: 0.000687
Trapezoid method: 0.000677
Trapezoid method: 0.000666
Trapezoid method: 0.000656
Trapezoid method: 0.000646
Trapezoid method: 0.000636
Trapezoid method: 0.000626
Trapezoid method: 0.000616
Trapezoid method: 0.000607
Trapezoid method: 0.000597
Trapezoid method: 0.000588
Trapezoid method: 0.000579
Trapezoid method: 0.000570
Trapezoid method: 0.000561
Trapezoid method: 0.000552
Trapezoid method: 0.000543
Trapezoid method: 0.000534
Trapezoid method: 0.000526
Trapezoid method: 0.000518
Trapezoid method: 0.000509
Trapezoid method: 0.000501
Trapezoid method: 0.000493
Trapezoid method: 0.000485
Trapezoid method: 0.000477
Trapezoid method: 0.000470
Trapezoid method: 0.000462
Trapezoid method: 0.000455
Trapezoid method: 0.000447
Trapezoid method: 0.000440
Trapezoid method: 0.000433
Trapezoid method: 0.000426
Trapezoid method: 0.000419
Trapezoid method: 0.000412
Trapezoid method: 0.000406
Trapezoid method: 0.000399
Trapezoid method: 0.000392
Trapezoid method: 0.000386
Trapezoid method: 0.000380
Trapezoid method: 0.000373
Trapezoid method: 0.000367
Trapezoid method: 0.000361
Trapezoid method: 0.000355
Trapezoid method: 0.000349
Trapezoid method: 0.000344
Trapezoid method: 0.000338
Trapezoid method: 0.000332
Trapezoid method: 0.000327
Trapezoid method: 0.000321
Trapezoid method: 0.000316
Trapezoid method: 0.000311
Trapezoid method: 0.000306
Trapezoid method: 0.000301
Trapezoid method: 0.000296
Trapezoid method: 0.000291
Trapezoid method: 0.000286
Trapezoid method: 0.000281
Trapezoid method: 0.000276
Trapezoid method: 0.000272
Trapezoid method: 0.000267
Trapezoid method: 0.000263
Trapezoid method: 0.000258
Trapezoid method: 0.000254
Trapezoid method: 0.000250
Trapezoid method: 0.000245
Trapezoid method: 0.000241
Trapezoid method: 0.000237
Trapezoid method: 0.000233
Trapezoid method: 0.000229
Trapezoid method: 0.000225
Trapezoid method: 0.000222
Trapezoid method: 0.000218
Trapezoid method: 0.000214
Trapezoid method: 0.000210
Trapezoid method: 0.000207
Trapezoid method: 0.000203
Trapezoid method: 0.000200
Trapezoid method: 0.000197
Trapezoid method: 0.000193
Trapezoid method: 0.000190
Trapezoid method: 0.000187
Trapezoid method: 0.000183
Trapezoid method: 0.000180
Trapezoid method: 0.000177
Trapezoid method: 0.000174
Trapezoid method: 0.000171
Trapezoid method: 0.000168
Trapezoid method: 0.000165
Trapezoid method: 0.000163
Trapezoid method: 0.000160
Trapezoid method: 0.000157
Trapezoid method: 0.000154
Trapezoid method: 0.000152
Trapezoid method: 0.000149
Trapezoid method: 0.000147
Trapezoid method: 0.000144
Trapezoid method: 0.000142
Trapezoid method: 0.000139
Trapezoid method: 0.000137
Trapezoid method: 0.000134
Trapezoid method: 0.000132
Trapezoid method: 0.000130
Trapezoid method: 0.000128
Trapezoid method: 0.000125
Trapezoid method: 0.000123
Trapezoid method: 0.000121
Trapezoid method: 0.000119
Trapezoid method: 0.000117
Trapezoid method: 0.000115
Trapezoid method: 0.000113
Trapezoid method: 0.000111
Trapezoid method: 0.000109
Trapezoid method: 0.000107
Trapezoid method: 0.000105
Trapezoid method: 0.000104
Trapezoid method: 0.000102
Trapezoid method: 0.000100
Trapezoid method: 0.000098
Trapezoid method: 0.000097
Trapezoid method: 0.000095
Trapezoid method: 0.000093
Trapezoid method: 0.000092
Trapezoid method: 0.000090
Trapezoid method: 0.000089
Trapezoid method: 0.000087
Trapezoid method: 0.000086
Trapezoid method: 0.000084
Trapezoid method: 0.000083
Trapezoid method: 0.000081
Trapezoid method: 0.000080
Trapezoid method: 0.000078
Trapezoid method: 0.000077
Trapezoid method: 0.000076
Trapezoid method: 0.000074
Trapezoid method: 0.000073
Trapezoid method: 0.000072
Trapezoid method: 0.000071
Trapezoid method: 0.000069
Trapezoid method: 0.000068
Trapezoid method: 0.000067
Trapezoid method: 0.000066
Trapezoid method: 0.000065
Trapezoid method: 0.000064
Trapezoid method: 0.000063
Trapezoid method: 0.000062
Trapezoid method: 0.000060
Trapezoid method: 0.000059
Trapezoid method: 0.000058
Trapezoid method: 0.000057
Trapezoid method: 0.000056
Trapezoid method: 0.000055
Trapezoid method: 0.000054
Trapezoid method: 0.000054
Trapezoid method: 0.000053
Trapezoid method: 0.000052
Trapezoid method: 0.000051
Trapezoid method: 0.000050
Trapezoid method: 0.000049
Trapezoid method: 0.000048
Trapezoid method: 0.000047
Trapezoid method: 0.000047
Trapezoid method: 0.000046
Trapezoid method: 0.000045
Trapezoid method: 0.000044
Trapezoid method: 0.000043
Trapezoid method: 0.000043
Trapezoid method: 0.000042
Trapezoid method: 0.000041
Trapezoid method: 0.000041
Trapezoid method: 0.000040
Trapezoid method: 0.000039
Trapezoid method: 0.000039
Trapezoid method: 0.000038
Trapezoid method: 0.000037
Trapezoid method: 0.000037
Trapezoid method: 0.000036
Trapezoid method: 0.000035
Trapezoid method: 0.000035
Trapezoid method: 0.000034
Trapezoid method: 0.000034
Trapezoid method: 0.000033
Trapezoid method: 0.000032
Trapezoid method: 0.000032
Trapezoid method: 0.000031
Trapezoid method: 0.000031
Trapezoid method: 0.000030
Trapezoid method: 0.000030
Trapezoid method: 0.000029
Trapezoid method: 0.000029
Trapezoid method: 0.000028
Trapezoid method: 0.000028
Trapezoid method: 0.000027
Trapezoid method: 0.000027
Trapezoid method: 0.000026
Trapezoid method: 0.000026
Trapezoid method: 0.000026
Trapezoid method: 0.000025
Trapezoid method: 0.000025
Trapezoid method: 0.000024
Trapezoid method: 0.000024
Trapezoid method: 0.000023
Trapezoid method: 0.000023
Trapezoid method: 0.000023
Trapezoid method: 0.000022
Trapezoid method: 0.000022
Trapezoid method: 0.000022
Trapezoid method: 0.000021
Trapezoid method: 0.000021
Trapezoid method: 0.000020
Trapezoid method: 0.000020
Trapezoid method: 0.000020
Trapezoid method: 0.000019
Trapezoid method: 0.000019
Trapezoid method: 0.000019
Trapezoid method: 0.000019
Trapezoid method: 0.000018
Trapezoid method: 0.000018
Trapezoid method: 0.000018
Trapezoid method: 0.000017
Trapezoid method: 0.000017
Trapezoid method: 0.000017
Trapezoid method: 0.000016
Trapezoid method: 0.000016
Trapezoid method: 0.000016
Trapezoid method: 0.000016
Trapezoid method: 0.000015
Trapezoid method: 0.000015
Trapezoid method: 0.000015
Trapezoid method: 0.000015
Trapezoid method: 0.000014
Trapezoid method: 0.000014
Trapezoid method: 0.000014
Trapezoid method: 0.000014
Trapezoid method: 0.000013
Trapezoid method: 0.000013
Trapezoid method: 0.000013
Trapezoid method: 0.000013
Trapezoid method: 0.000013
Trapezoid method: 0.000012
Trapezoid method: 0.000012
Trapezoid method: 0.000012
Trapezoid method: 0.000012
Trapezoid method: 0.000012
Trapezoid method: 0.000011
Trapezoid method: 0.000011
Trapezoid method: 0.000011
Trapezoid method: 0.000011
Trapezoid method: 0.000011
Trapezoid method: 0.000010
Trapezoid method: 0.000010
Trapezoid method: 0.000010
Trapezoid method: 0.000010
Trapezoid method: 0.000010
Trapezoid method: 0.000010
Trapezoid method: 0.000010
Trapezoid method: 0.000009
Trapezoid method: 0.000009
Trapezoid method: 0.000009
Trapezoid method: 0.000009
Trapezoid method: 0.000009
Trapezoid method: 0.000009
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
fprintf('Simpson''s composite method: %f\n', t_simp);
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000008
Simpson's composite method: 0.000008
Simpson's composite method: 0.000008
Simpson's composite method: 0.000008
Simpson's composite method: 0.000008
Simpson's composite method: 0.000008
Simpson's composite method: 0.000008
Simpson's composite method: 0.000008
Simpson's composite method: 0.000009
Simpson's composite method: 0.000009
Simpson's composite method: 0.000009
Simpson's composite method: 0.000009
Simpson's composite method: 0.000009
Simpson's composite method: 0.000009
Simpson's composite method: 0.000010
Simpson's composite method: 0.000010
Simpson's composite method: 0.000010
Simpson's composite method: 0.000010
Simpson's composite method: 0.000010
Simpson's composite method: 0.000010
Simpson's composite method: 0.000010
Simpson's composite method: 0.000011
Simpson's composite method: 0.000011
Simpson's composite method: 0.000011
Simpson's composite method: 0.000011
Simpson's composite method: 0.000011
Simpson's composite method: 0.000012
Simpson's composite method: 0.000012
Simpson's composite method: 0.000012
Simpson's composite method: 0.000012
Simpson's composite method: 0.000012
Simpson's composite method: 0.000013
Simpson's composite method: 0.000013
Simpson's composite method: 0.000013
Simpson's composite method: 0.000013
Simpson's composite method: 0.000013
Simpson's composite method: 0.000014
Simpson's composite method: 0.000014
Simpson's composite method: 0.000014
Simpson's composite method: 0.000014
Simpson's composite method: 0.000015
Simpson's composite method: 0.000015
Simpson's composite method: 0.000015
Simpson's composite method: 0.000015
Simpson's composite method: 0.000016
Simpson's composite method: 0.000016
Simpson's composite method: 0.000016
Simpson's composite method: 0.000016
Simpson's composite method: 0.000017
Simpson's composite method: 0.000017
Simpson's composite method: 0.000017
Simpson's composite method: 0.000018
Simpson's composite method: 0.000018
Simpson's composite method: 0.000018
Simpson's composite method: 0.000019
Simpson's composite method: 0.000019
Simpson's composite method: 0.000019
Simpson's composite method: 0.000019
Simpson's composite method: 0.000020
Simpson's composite method: 0.000020
Simpson's composite method: 0.000020
Simpson's composite method: 0.000021
Simpson's composite method: 0.000021
Simpson's composite method: 0.000022
Simpson's composite method: 0.000022
Simpson's composite method: 0.000022
Simpson's composite method: 0.000023
Simpson's composite method: 0.000023
Simpson's composite method: 0.000023
Simpson's composite method: 0.000024
Simpson's composite method: 0.000024
Simpson's composite method: 0.000025
Simpson's composite method: 0.000025
Simpson's composite method: 0.000026
Simpson's composite method: 0.000026
Simpson's composite method: 0.000026
Simpson's composite method: 0.000027
Simpson's composite method: 0.000027
Simpson's composite method: 0.000028
Simpson's composite method: 0.000028
Simpson's composite method: 0.000029
Simpson's composite method: 0.000029
Simpson's composite method: 0.000030
Simpson's composite method: 0.000030
Simpson's composite method: 0.000031
Simpson's composite method: 0.000031
Simpson's composite method: 0.000032
Simpson's composite method: 0.000032
Simpson's composite method: 0.000033
Simpson's composite method: 0.000034
Simpson's composite method: 0.000034
Simpson's composite method: 0.000035
Simpson's composite method: 0.000035
Simpson's composite method: 0.000036
Simpson's composite method: 0.000037
Simpson's composite method: 0.000037
Simpson's composite method: 0.000038
Simpson's composite method: 0.000039
Simpson's composite method: 0.000039
Simpson's composite method: 0.000040
Simpson's composite method: 0.000041
Simpson's composite method: 0.000041
Simpson's composite method: 0.000042
Simpson's composite method: 0.000043
Simpson's composite method: 0.000043
Simpson's composite method: 0.000044
Simpson's composite method: 0.000045
Simpson's composite method: 0.000046
Simpson's composite method: 0.000047
Simpson's composite method: 0.000047
Simpson's composite method: 0.000048
Simpson's composite method: 0.000049
Simpson's composite method: 0.000050
Simpson's composite method: 0.000051
Simpson's composite method: 0.000052
Simpson's composite method: 0.000053
Simpson's composite method: 0.000054
Simpson's composite method: 0.000054
Simpson's composite method: 0.000055
Simpson's composite method: 0.000056
Simpson's composite method: 0.000057
Simpson's composite method: 0.000058
Simpson's composite method: 0.000059
Simpson's composite method: 0.000060
Simpson's composite method: 0.000062
Simpson's composite method: 0.000063
Simpson's composite method: 0.000064
Simpson's composite method: 0.000065
Simpson's composite method: 0.000066
Simpson's composite method: 0.000067
Simpson's composite method: 0.000068
Simpson's composite method: 0.000069
Simpson's composite method: 0.000071
Simpson's composite method: 0.000072
Simpson's composite method: 0.000073
Simpson's composite method: 0.000074
Simpson's composite method: 0.000076
Simpson's composite method: 0.000077
Simpson's composite method: 0.000078
Simpson's composite method: 0.000080
Simpson's composite method: 0.000081
Simpson's composite method: 0.000083
Simpson's composite method: 0.000084
Simpson's composite method: 0.000086
Simpson's composite method: 0.000087
Simpson's composite method: 0.000089
Simpson's composite method: 0.000090
Simpson's composite method: 0.000092
Simpson's composite method: 0.000093
Simpson's composite method: 0.000095
Simpson's composite method: 0.000097
Simpson's composite method: 0.000098
Simpson's composite method: 0.000100
Simpson's composite method: 0.000102
Simpson's composite method: 0.000104
Simpson's composite method: 0.000105
Simpson's composite method: 0.000107
Simpson's composite method: 0.000109
Simpson's composite method: 0.000111
Simpson's composite method: 0.000113
Simpson's composite method: 0.000115
Simpson's composite method: 0.000117
Simpson's composite method: 0.000119
Simpson's composite method: 0.000121
Simpson's composite method: 0.000123
Simpson's composite method: 0.000125
Simpson's composite method: 0.000128
Simpson's composite method: 0.000130
Simpson's composite method: 0.000132
Simpson's composite method: 0.000134
Simpson's composite method: 0.000137
Simpson's composite method: 0.000139
Simpson's composite method: 0.000142
Simpson's composite method: 0.000144
Simpson's composite method: 0.000147
Simpson's composite method: 0.000149
Simpson's composite method: 0.000152
Simpson's composite method: 0.000154
Simpson's composite method: 0.000157
Simpson's composite method: 0.000160
Simpson's composite method: 0.000163
Simpson's composite method: 0.000165
Simpson's composite method: 0.000168
Simpson's composite method: 0.000171
Simpson's composite method: 0.000174
Simpson's composite method: 0.000177
Simpson's composite method: 0.000180
Simpson's composite method: 0.000183
Simpson's composite method: 0.000187
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Simpson's composite method: 0.000193
Simpson's composite method: 0.000197
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Simpson's composite method: 0.000203
Simpson's composite method: 0.000207
Simpson's composite method: 0.000210
Simpson's composite method: 0.000214
Simpson's composite method: 0.000218
Simpson's composite method: 0.000222
Simpson's composite method: 0.000225
Simpson's composite method: 0.000229
Simpson's composite method: 0.000233
Simpson's composite method: 0.000237
Simpson's composite method: 0.000241
Simpson's composite method: 0.000245
Simpson's composite method: 0.000250
Simpson's composite method: 0.000254
Simpson's composite method: 0.000258
Simpson's composite method: 0.000263
Simpson's composite method: 0.000267
Simpson's composite method: 0.000272
Simpson's composite method: 0.000276
Simpson's composite method: 0.000281
Simpson's composite method: 0.000286
Simpson's composite method: 0.000291
Simpson's composite method: 0.000296
Simpson's composite method: 0.000301
Simpson's composite method: 0.000306
Simpson's composite method: 0.000311
Simpson's composite method: 0.000316
Simpson's composite method: 0.000321
Simpson's composite method: 0.000327
Simpson's composite method: 0.000332
Simpson's composite method: 0.000338
Simpson's composite method: 0.000344
Simpson's composite method: 0.000349
Simpson's composite method: 0.000355
Simpson's composite method: 0.000361
Simpson's composite method: 0.000367
Simpson's composite method: 0.000373
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Simpson's composite method: 0.000386
Simpson's composite method: 0.000392
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Simpson's composite method: 0.000406
Simpson's composite method: 0.000412
Simpson's composite method: 0.000419
Simpson's composite method: 0.000426
Simpson's composite method: 0.000433
Simpson's composite method: 0.000440
Simpson's composite method: 0.000447
Simpson's composite method: 0.000455
Simpson's composite method: 0.000462
Simpson's composite method: 0.000470
Simpson's composite method: 0.000477
Simpson's composite method: 0.000485
Simpson's composite method: 0.000493
Simpson's composite method: 0.000501
Simpson's composite method: 0.000509
Simpson's composite method: 0.000518
Simpson's composite method: 0.000526
Simpson's composite method: 0.000534
Simpson's composite method: 0.000543
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Simpson's composite method: 0.000561
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Simpson's composite method: 0.000579
Simpson's composite method: 0.000588
Simpson's composite method: 0.000597
Simpson's composite method: 0.000607
Simpson's composite method: 0.000616
Simpson's composite method: 0.000626
Simpson's composite method: 0.000636
Simpson's composite method: 0.000646
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Simpson's composite method: 0.000666
Simpson's composite method: 0.000677
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Simpson's composite method: 0.000698
Simpson's composite method: 0.000709
Simpson's composite method: 0.000720
Simpson's composite method: 0.000731
Simpson's composite method: 0.000742
Simpson's composite method: 0.000754
Simpson's composite method: 0.000765
Simpson's composite method: 0.000777
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Simpson's composite method: 0.000801
Simpson's composite method: 0.000813
Simpson's composite method: 0.000825
Simpson's composite method: 0.000837
Simpson's composite method: 0.000850
Simpson's composite method: 0.000863
Simpson's composite method: 0.000876
Simpson's composite method: 0.000889
Simpson's composite method: 0.000902
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Simpson's composite method: 0.000929
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Simpson's composite method: 0.000956
Simpson's composite method: 0.000970
Simpson's composite method: 0.000984
Simpson's composite method: 0.000999
Simpson's composite method: 0.001013
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Simpson's composite method: 0.001042
Simpson's composite method: 0.001057
Simpson's composite method: 0.001072
Simpson's composite method: 0.001088
Simpson's composite method: 0.001103
Simpson's composite method: 0.001119
Simpson's composite method: 0.001134
Simpson's composite method: 0.001150
Simpson's composite method: 0.001166
Simpson's composite method: 0.001182
Simpson's composite method: 0.001199
Simpson's composite method: 0.001215
Simpson's composite method: 0.001232
Simpson's composite method: 0.001249
Simpson's composite method: 0.001266
Simpson's composite method: 0.001283
Simpson's composite method: 0.001300
Simpson's composite method: 0.001318
Simpson's composite method: 0.001336
Simpson's composite method: 0.001353
Simpson's composite method: 0.001371
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Simpson's composite method: 0.001408
Simpson's composite method: 0.001426
Simpson's composite method: 0.001445
Simpson's composite method: 0.001463
Simpson's composite method: 0.001482
Simpson's composite method: 0.001501
Simpson's composite method: 0.001520
Simpson's composite method: 0.001540
Simpson's composite method: 0.001559
Simpson's composite method: 0.001579
Simpson's composite method: 0.001599
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Simpson's composite method: 0.001638
Simpson's composite method: 0.001659
Simpson's composite method: 0.001679
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Simpson's composite method: 0.001720
Simpson's composite method: 0.001741
Simpson's composite method: 0.001761
Simpson's composite method: 0.001782
Simpson's composite method: 0.001803
Simpson's composite method: 0.001825
Simpson's composite method: 0.001846
Simpson's composite method: 0.001867
Simpson's composite method: 0.001889
Simpson's composite method: 0.001911
Simpson's composite method: 0.001932
Simpson's composite method: 0.001954
Simpson's composite method: 0.001976
Simpson's composite method: 0.001998
Simpson's composite method: 0.002020
Simpson's composite method: 0.002043
Simpson's composite method: 0.002065
Simpson's composite method: 0.002087
Simpson's composite method: 0.002110
Simpson's composite method: 0.002132
Simpson's composite method: 0.002155
Simpson's composite method: 0.002178
Simpson's composite method: 0.002200
Simpson's composite method: 0.002223
Simpson's composite method: 0.002246
Simpson's composite method: 0.002269
Simpson's composite method: 0.002292
Simpson's composite method: 0.002315
Simpson's composite method: 0.002338
Simpson's composite method: 0.002361
Simpson's composite method: 0.002384
Simpson's composite method: 0.002408
Simpson's composite method: 0.002431
Simpson's composite method: 0.002454
Simpson's composite method: 0.002477
Simpson's composite method: 0.002500
Simpson's composite method: 0.002524
Simpson's composite method: 0.002547
Simpson's composite method: 0.002570
Simpson's composite method: 0.002593
Simpson's composite method: 0.002616
Simpson's composite method: 0.002640
Simpson's composite method: 0.002663
Simpson's composite method: 0.002686
Simpson's composite method: 0.002709
Simpson's composite method: 0.002732
Simpson's composite method: 0.002755
Simpson's composite method: 0.002778
Simpson's composite method: 0.002800
Simpson's composite method: 0.002823
Simpson's composite method: 0.002846
Simpson's composite method: 0.002868
Simpson's composite method: 0.002891
Simpson's composite method: 0.002913
Simpson's composite method: 0.002936
Simpson's composite method: 0.002958
Simpson's composite method: 0.002980
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Simpson's composite method: 0.003024
Simpson's composite method: 0.003045
Simpson's composite method: 0.003067
Simpson's composite method: 0.003088
Simpson's composite method: 0.003110
Simpson's composite method: 0.003131
Simpson's composite method: 0.003152
Simpson's composite method: 0.003172
Simpson's composite method: 0.003193
Simpson's composite method: 0.003213
Simpson's composite method: 0.003234
Simpson's composite method: 0.003254
Simpson's composite method: 0.003273
Simpson's composite method: 0.003293
Simpson's composite method: 0.003312
Simpson's composite method: 0.003332
Simpson's composite method: 0.003351
Simpson's composite method: 0.003369
Simpson's composite method: 0.003388
Simpson's composite method: 0.003406
Simpson's composite method: 0.003424
Simpson's composite method: 0.003442
Simpson's composite method: 0.003459
Simpson's composite method: 0.003476
Simpson's composite method: 0.003493
Simpson's composite method: 0.003510
Simpson's composite method: 0.003526
Simpson's composite method: 0.003542
Simpson's composite method: 0.003558
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Simpson's composite method: 0.003603
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Simpson's composite method: 0.003698
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Simpson's composite method: 0.003722
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Simpson's composite method: 0.003744
Simpson's composite method: 0.003755
Simpson's composite method: 0.003765
Simpson's composite method: 0.003775
Simpson's composite method: 0.003784
Simpson's composite method: 0.003794
Simpson's composite method: 0.003802
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Simpson's composite method: 0.003819
Simpson's composite method: 0.003826
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Simpson's composite method: 0.003852
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Simpson's composite method: 0.003863
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Simpson's composite method: 0.003872
Simpson's composite method: 0.003876
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Simpson's composite method: 0.003890
Simpson's composite method: 0.003891
Simpson's composite method: 0.003891
Simpson's composite method: 0.003891
Simpson's composite method: 0.003891
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Simpson's composite method: 0.003887
Simpson's composite method: 0.003885
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Simpson's composite method: 0.003872
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Simpson's composite method: 0.003775
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Simpson's composite method: 0.003722
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Simpson's composite method: 0.000272
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Simpson's composite method: 0.000064
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Simpson's composite method: 0.000062
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Simpson's composite method: 0.000038
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Simpson's composite method: 0.000037
Simpson's composite method: 0.000036
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Simpson's composite method: 0.000032
Simpson's composite method: 0.000032
Simpson's composite method: 0.000031
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Simpson's composite method: 0.000030
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Simpson's composite method: 0.000029
Simpson's composite method: 0.000029
Simpson's composite method: 0.000028
Simpson's composite method: 0.000028
Simpson's composite method: 0.000027
Simpson's composite method: 0.000027
Simpson's composite method: 0.000026
Simpson's composite method: 0.000026
Simpson's composite method: 0.000026
Simpson's composite method: 0.000025
Simpson's composite method: 0.000025
Simpson's composite method: 0.000024
Simpson's composite method: 0.000024
Simpson's composite method: 0.000023
Simpson's composite method: 0.000023
Simpson's composite method: 0.000023
Simpson's composite method: 0.000022
Simpson's composite method: 0.000022
Simpson's composite method: 0.000022
Simpson's composite method: 0.000021
Simpson's composite method: 0.000021
Simpson's composite method: 0.000020
Simpson's composite method: 0.000020
Simpson's composite method: 0.000020
Simpson's composite method: 0.000019
Simpson's composite method: 0.000019
Simpson's composite method: 0.000019
Simpson's composite method: 0.000019
Simpson's composite method: 0.000018
Simpson's composite method: 0.000018
Simpson's composite method: 0.000018
Simpson's composite method: 0.000017
Simpson's composite method: 0.000017
Simpson's composite method: 0.000017
Simpson's composite method: 0.000016
Simpson's composite method: 0.000016
Simpson's composite method: 0.000016
Simpson's composite method: 0.000016
Simpson's composite method: 0.000015
Simpson's composite method: 0.000015
Simpson's composite method: 0.000015
Simpson's composite method: 0.000015
Simpson's composite method: 0.000014
Simpson's composite method: 0.000014
Simpson's composite method: 0.000014
Simpson's composite method: 0.000014
Simpson's composite method: 0.000013
Simpson's composite method: 0.000013
Simpson's composite method: 0.000013
Simpson's composite method: 0.000013
Simpson's composite method: 0.000013
Simpson's composite method: 0.000012
Simpson's composite method: 0.000012
Simpson's composite method: 0.000012
Simpson's composite method: 0.000012
Simpson's composite method: 0.000012
Simpson's composite method: 0.000011
Simpson's composite method: 0.000011
Simpson's composite method: 0.000011
Simpson's composite method: 0.000011
Simpson's composite method: 0.000011
Simpson's composite method: 0.000010
Simpson's composite method: 0.000010
Simpson's composite method: 0.000010
Simpson's composite method: 0.000010
Simpson's composite method: 0.000010
Simpson's composite method: 0.000010
Simpson's composite method: 0.000010
Simpson's composite method: 0.000009
Simpson's composite method: 0.000009
Simpson's composite method: 0.000009
Simpson's composite method: 0.000009
Simpson's composite method: 0.000009
Simpson's composite method: 0.000009
Simpson's composite method: 0.000008
Simpson's composite method: 0.000008
Simpson's composite method: 0.000008
Simpson's composite method: 0.000008
Simpson's composite method: 0.000008
Simpson's composite method: 0.000008
Simpson's composite method: 0.000008
Simpson's composite method: 0.000008
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
fprintf('Exact value: %f\n', t_exact);
Exact value: 1.000000
fprintf('\nNormal distribution integral:\n');
Normal distribution integral:
fprintf('Trapezoid method: %f\n', norm_trap);
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000003
Trapezoid method: 0.000003
Trapezoid method: 0.000003
Trapezoid method: 0.000003
Trapezoid method: 0.000003
Trapezoid method: 0.000003
Trapezoid method: 0.000003
Trapezoid method: 0.000003
Trapezoid method: 0.000003
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000009
Trapezoid method: 0.000009
Trapezoid method: 0.000009
Trapezoid method: 0.000010
Trapezoid method: 0.000010
Trapezoid method: 0.000010
Trapezoid method: 0.000011
Trapezoid method: 0.000011
Trapezoid method: 0.000011
Trapezoid method: 0.000012
Trapezoid method: 0.000012
Trapezoid method: 0.000013
Trapezoid method: 0.000013
Trapezoid method: 0.000013
Trapezoid method: 0.000014
Trapezoid method: 0.000014
Trapezoid method: 0.000015
Trapezoid method: 0.000015
Trapezoid method: 0.000016
Trapezoid method: 0.000016
Trapezoid method: 0.000017
Trapezoid method: 0.000018
Trapezoid method: 0.000018
Trapezoid method: 0.000019
Trapezoid method: 0.000019
Trapezoid method: 0.000020
Trapezoid method: 0.000021
Trapezoid method: 0.000021
Trapezoid method: 0.000022
Trapezoid method: 0.000023
Trapezoid method: 0.000023
Trapezoid method: 0.000024
Trapezoid method: 0.000025
Trapezoid method: 0.000026
Trapezoid method: 0.000027
Trapezoid method: 0.000028
Trapezoid method: 0.000028
Trapezoid method: 0.000029
Trapezoid method: 0.000030
Trapezoid method: 0.000031
Trapezoid method: 0.000032
Trapezoid method: 0.000033
Trapezoid method: 0.000034
Trapezoid method: 0.000035
Trapezoid method: 0.000036
Trapezoid method: 0.000038
Trapezoid method: 0.000039
Trapezoid method: 0.000040
Trapezoid method: 0.000041
Trapezoid method: 0.000042
Trapezoid method: 0.000044
Trapezoid method: 0.000045
Trapezoid method: 0.000046
Trapezoid method: 0.000048
Trapezoid method: 0.000049
Trapezoid method: 0.000051
Trapezoid method: 0.000052
Trapezoid method: 0.000054
Trapezoid method: 0.000055
Trapezoid method: 0.000057
Trapezoid method: 0.000059
Trapezoid method: 0.000060
Trapezoid method: 0.000062
Trapezoid method: 0.000064
Trapezoid method: 0.000066
Trapezoid method: 0.000068
Trapezoid method: 0.000070
Trapezoid method: 0.000072
Trapezoid method: 0.000074
Trapezoid method: 0.000076
Trapezoid method: 0.000078
Trapezoid method: 0.000080
Trapezoid method: 0.000083
Trapezoid method: 0.000085
Trapezoid method: 0.000087
Trapezoid method: 0.000090
Trapezoid method: 0.000092
Trapezoid method: 0.000095
Trapezoid method: 0.000097
Trapezoid method: 0.000100
Trapezoid method: 0.000103
Trapezoid method: 0.000106
Trapezoid method: 0.000109
Trapezoid method: 0.000111
Trapezoid method: 0.000114
Trapezoid method: 0.000118
Trapezoid method: 0.000121
Trapezoid method: 0.000124
Trapezoid method: 0.000127
Trapezoid method: 0.000131
Trapezoid method: 0.000134
Trapezoid method: 0.000138
Trapezoid method: 0.000141
Trapezoid method: 0.000145
Trapezoid method: 0.000149
Trapezoid method: 0.000153
Trapezoid method: 0.000156
Trapezoid method: 0.000161
Trapezoid method: 0.000165
Trapezoid method: 0.000169
Trapezoid method: 0.000173
Trapezoid method: 0.000177
Trapezoid method: 0.000182
Trapezoid method: 0.000187
Trapezoid method: 0.000191
Trapezoid method: 0.000196
Trapezoid method: 0.000201
Trapezoid method: 0.000206
Trapezoid method: 0.000211
Trapezoid method: 0.000216
Trapezoid method: 0.000221
Trapezoid method: 0.000227
Trapezoid method: 0.000232
Trapezoid method: 0.000238
Trapezoid method: 0.000243
Trapezoid method: 0.000249
Trapezoid method: 0.000255
Trapezoid method: 0.000261
Trapezoid method: 0.000267
Trapezoid method: 0.000274
Trapezoid method: 0.000280
Trapezoid method: 0.000287
Trapezoid method: 0.000293
Trapezoid method: 0.000300
Trapezoid method: 0.000307
Trapezoid method: 0.000314
Trapezoid method: 0.000321
Trapezoid method: 0.000328
Trapezoid method: 0.000336
Trapezoid method: 0.000343
Trapezoid method: 0.000351
Trapezoid method: 0.000359
Trapezoid method: 0.000367
Trapezoid method: 0.000375
Trapezoid method: 0.000383
Trapezoid method: 0.000391
Trapezoid method: 0.000400
Trapezoid method: 0.000408
Trapezoid method: 0.000417
Trapezoid method: 0.000426
Trapezoid method: 0.000435
Trapezoid method: 0.000444
Trapezoid method: 0.000454
Trapezoid method: 0.000463
Trapezoid method: 0.000473
Trapezoid method: 0.000483
Trapezoid method: 0.000493
Trapezoid method: 0.000503
Trapezoid method: 0.000513
Trapezoid method: 0.000524
Trapezoid method: 0.000535
Trapezoid method: 0.000545
Trapezoid method: 0.000556
Trapezoid method: 0.000567
Trapezoid method: 0.000579
Trapezoid method: 0.000590
Trapezoid method: 0.000602
Trapezoid method: 0.000614
Trapezoid method: 0.000626
Trapezoid method: 0.000638
Trapezoid method: 0.000650
Trapezoid method: 0.000662
Trapezoid method: 0.000675
Trapezoid method: 0.000688
Trapezoid method: 0.000701
Trapezoid method: 0.000714
Trapezoid method: 0.000727
Trapezoid method: 0.000741
Trapezoid method: 0.000755
Trapezoid method: 0.000768
Trapezoid method: 0.000782
Trapezoid method: 0.000797
Trapezoid method: 0.000811
Trapezoid method: 0.000826
Trapezoid method: 0.000840
Trapezoid method: 0.000855
Trapezoid method: 0.000870
Trapezoid method: 0.000886
Trapezoid method: 0.000901
Trapezoid method: 0.000917
Trapezoid method: 0.000933
Trapezoid method: 0.000949
Trapezoid method: 0.000965
Trapezoid method: 0.000981
Trapezoid method: 0.000998
Trapezoid method: 0.001014
Trapezoid method: 0.001031
Trapezoid method: 0.001048
Trapezoid method: 0.001065
Trapezoid method: 0.001083
Trapezoid method: 0.001100
Trapezoid method: 0.001118
Trapezoid method: 0.001136
Trapezoid method: 0.001154
Trapezoid method: 0.001172
Trapezoid method: 0.001191
Trapezoid method: 0.001209
Trapezoid method: 0.001228
Trapezoid method: 0.001247
Trapezoid method: 0.001266
Trapezoid method: 0.001286
Trapezoid method: 0.001305
Trapezoid method: 0.001325
Trapezoid method: 0.001344
Trapezoid method: 0.001364
Trapezoid method: 0.001384
Trapezoid method: 0.001404
Trapezoid method: 0.001425
Trapezoid method: 0.001445
Trapezoid method: 0.001466
Trapezoid method: 0.001487
Trapezoid method: 0.001508
Trapezoid method: 0.001529
Trapezoid method: 0.001550
Trapezoid method: 0.001572
Trapezoid method: 0.001593
Trapezoid method: 0.001615
Trapezoid method: 0.001636
Trapezoid method: 0.001658
Trapezoid method: 0.001680
Trapezoid method: 0.001703
Trapezoid method: 0.001725
Trapezoid method: 0.001747
Trapezoid method: 0.001770
Trapezoid method: 0.001792
Trapezoid method: 0.001815
Trapezoid method: 0.001838
Trapezoid method: 0.001861
Trapezoid method: 0.001884
Trapezoid method: 0.001907
Trapezoid method: 0.001930
Trapezoid method: 0.001954
Trapezoid method: 0.001977
Trapezoid method: 0.002000
Trapezoid method: 0.002024
Trapezoid method: 0.002048
Trapezoid method: 0.002071
Trapezoid method: 0.002095
Trapezoid method: 0.002119
Trapezoid method: 0.002143
Trapezoid method: 0.002167
Trapezoid method: 0.002191
Trapezoid method: 0.002215
Trapezoid method: 0.002239
Trapezoid method: 0.002263
Trapezoid method: 0.002287
Trapezoid method: 0.002311
Trapezoid method: 0.002335
Trapezoid method: 0.002359
Trapezoid method: 0.002383
Trapezoid method: 0.002408
Trapezoid method: 0.002432
Trapezoid method: 0.002456
Trapezoid method: 0.002480
Trapezoid method: 0.002504
Trapezoid method: 0.002529
Trapezoid method: 0.002553
Trapezoid method: 0.002577
Trapezoid method: 0.002601
Trapezoid method: 0.002625
Trapezoid method: 0.002649
Trapezoid method: 0.002673
Trapezoid method: 0.002697
Trapezoid method: 0.002721
Trapezoid method: 0.002744
Trapezoid method: 0.002768
Trapezoid method: 0.002792
Trapezoid method: 0.002815
Trapezoid method: 0.002839
Trapezoid method: 0.002862
Trapezoid method: 0.002885
Trapezoid method: 0.002908
Trapezoid method: 0.002932
Trapezoid method: 0.002954
Trapezoid method: 0.002977
Trapezoid method: 0.003000
Trapezoid method: 0.003023
Trapezoid method: 0.003045
Trapezoid method: 0.003067
Trapezoid method: 0.003090
Trapezoid method: 0.003112
Trapezoid method: 0.003133
Trapezoid method: 0.003155
Trapezoid method: 0.003177
Trapezoid method: 0.003198
Trapezoid method: 0.003219
Trapezoid method: 0.003240
Trapezoid method: 0.003261
Trapezoid method: 0.003282
Trapezoid method: 0.003302
Trapezoid method: 0.003322
Trapezoid method: 0.003342
Trapezoid method: 0.003362
Trapezoid method: 0.003382
Trapezoid method: 0.003401
Trapezoid method: 0.003420
Trapezoid method: 0.003439
Trapezoid method: 0.003457
Trapezoid method: 0.003476
Trapezoid method: 0.003494
Trapezoid method: 0.003512
Trapezoid method: 0.003529
Trapezoid method: 0.003547
Trapezoid method: 0.003564
Trapezoid method: 0.003581
Trapezoid method: 0.003597
Trapezoid method: 0.003613
Trapezoid method: 0.003629
Trapezoid method: 0.003645
Trapezoid method: 0.003660
Trapezoid method: 0.003675
Trapezoid method: 0.003690
Trapezoid method: 0.003704
Trapezoid method: 0.003719
Trapezoid method: 0.003732
Trapezoid method: 0.003746
Trapezoid method: 0.003759
Trapezoid method: 0.003772
Trapezoid method: 0.003784
Trapezoid method: 0.003796
Trapezoid method: 0.003808
Trapezoid method: 0.003820
Trapezoid method: 0.003831
Trapezoid method: 0.003841
Trapezoid method: 0.003852
Trapezoid method: 0.003862
Trapezoid method: 0.003871
Trapezoid method: 0.003881
Trapezoid method: 0.003890
Trapezoid method: 0.003898
Trapezoid method: 0.003906
Trapezoid method: 0.003914
Trapezoid method: 0.003922
Trapezoid method: 0.003929
Trapezoid method: 0.003935
Trapezoid method: 0.003942
Trapezoid method: 0.003948
Trapezoid method: 0.003953
Trapezoid method: 0.003958
Trapezoid method: 0.003963
Trapezoid method: 0.003967
Trapezoid method: 0.003971
Trapezoid method: 0.003975
Trapezoid method: 0.003978
Trapezoid method: 0.003981
Trapezoid method: 0.003983
Trapezoid method: 0.003985
Trapezoid method: 0.003987
Trapezoid method: 0.003988
Trapezoid method: 0.003989
Trapezoid method: 0.003989
Trapezoid method: 0.003989
Trapezoid method: 0.003989
Trapezoid method: 0.003988
Trapezoid method: 0.003987
Trapezoid method: 0.003985
Trapezoid method: 0.003983
Trapezoid method: 0.003981
Trapezoid method: 0.003978
Trapezoid method: 0.003975
Trapezoid method: 0.003971
Trapezoid method: 0.003967
Trapezoid method: 0.003963
Trapezoid method: 0.003958
Trapezoid method: 0.003953
Trapezoid method: 0.003948
Trapezoid method: 0.003942
Trapezoid method: 0.003935
Trapezoid method: 0.003929
Trapezoid method: 0.003922
Trapezoid method: 0.003914
Trapezoid method: 0.003906
Trapezoid method: 0.003898
Trapezoid method: 0.003890
Trapezoid method: 0.003881
Trapezoid method: 0.003871
Trapezoid method: 0.003862
Trapezoid method: 0.003852
Trapezoid method: 0.003841
Trapezoid method: 0.003831
Trapezoid method: 0.003820
Trapezoid method: 0.003808
Trapezoid method: 0.003796
Trapezoid method: 0.003784
Trapezoid method: 0.003772
Trapezoid method: 0.003759
Trapezoid method: 0.003746
Trapezoid method: 0.003732
Trapezoid method: 0.003719
Trapezoid method: 0.003704
Trapezoid method: 0.003690
Trapezoid method: 0.003675
Trapezoid method: 0.003660
Trapezoid method: 0.003645
Trapezoid method: 0.003629
Trapezoid method: 0.003613
Trapezoid method: 0.003597
Trapezoid method: 0.003581
Trapezoid method: 0.003564
Trapezoid method: 0.003547
Trapezoid method: 0.003529
Trapezoid method: 0.003512
Trapezoid method: 0.003494
Trapezoid method: 0.003476
Trapezoid method: 0.003457
Trapezoid method: 0.003439
Trapezoid method: 0.003420
Trapezoid method: 0.003401
Trapezoid method: 0.003382
Trapezoid method: 0.003362
Trapezoid method: 0.003342
Trapezoid method: 0.003322
Trapezoid method: 0.003302
Trapezoid method: 0.003282
Trapezoid method: 0.003261
Trapezoid method: 0.003240
Trapezoid method: 0.003219
Trapezoid method: 0.003198
Trapezoid method: 0.003177
Trapezoid method: 0.003155
Trapezoid method: 0.003133
Trapezoid method: 0.003112
Trapezoid method: 0.003090
Trapezoid method: 0.003067
Trapezoid method: 0.003045
Trapezoid method: 0.003023
Trapezoid method: 0.003000
Trapezoid method: 0.002977
Trapezoid method: 0.002954
Trapezoid method: 0.002932
Trapezoid method: 0.002908
Trapezoid method: 0.002885
Trapezoid method: 0.002862
Trapezoid method: 0.002839
Trapezoid method: 0.002815
Trapezoid method: 0.002792
Trapezoid method: 0.002768
Trapezoid method: 0.002744
Trapezoid method: 0.002721
Trapezoid method: 0.002697
Trapezoid method: 0.002673
Trapezoid method: 0.002649
Trapezoid method: 0.002625
Trapezoid method: 0.002601
Trapezoid method: 0.002577
Trapezoid method: 0.002553
Trapezoid method: 0.002529
Trapezoid method: 0.002504
Trapezoid method: 0.002480
Trapezoid method: 0.002456
Trapezoid method: 0.002432
Trapezoid method: 0.002408
Trapezoid method: 0.002383
Trapezoid method: 0.002359
Trapezoid method: 0.002335
Trapezoid method: 0.002311
Trapezoid method: 0.002287
Trapezoid method: 0.002263
Trapezoid method: 0.002239
Trapezoid method: 0.002215
Trapezoid method: 0.002191
Trapezoid method: 0.002167
Trapezoid method: 0.002143
Trapezoid method: 0.002119
Trapezoid method: 0.002095
Trapezoid method: 0.002071
Trapezoid method: 0.002048
Trapezoid method: 0.002024
Trapezoid method: 0.002000
Trapezoid method: 0.001977
Trapezoid method: 0.001954
Trapezoid method: 0.001930
Trapezoid method: 0.001907
Trapezoid method: 0.001884
Trapezoid method: 0.001861
Trapezoid method: 0.001838
Trapezoid method: 0.001815
Trapezoid method: 0.001792
Trapezoid method: 0.001770
Trapezoid method: 0.001747
Trapezoid method: 0.001725
Trapezoid method: 0.001703
Trapezoid method: 0.001680
Trapezoid method: 0.001658
Trapezoid method: 0.001636
Trapezoid method: 0.001615
Trapezoid method: 0.001593
Trapezoid method: 0.001572
Trapezoid method: 0.001550
Trapezoid method: 0.001529
Trapezoid method: 0.001508
Trapezoid method: 0.001487
Trapezoid method: 0.001466
Trapezoid method: 0.001445
Trapezoid method: 0.001425
Trapezoid method: 0.001404
Trapezoid method: 0.001384
Trapezoid method: 0.001364
Trapezoid method: 0.001344
Trapezoid method: 0.001325
Trapezoid method: 0.001305
Trapezoid method: 0.001286
Trapezoid method: 0.001266
Trapezoid method: 0.001247
Trapezoid method: 0.001228
Trapezoid method: 0.001209
Trapezoid method: 0.001191
Trapezoid method: 0.001172
Trapezoid method: 0.001154
Trapezoid method: 0.001136
Trapezoid method: 0.001118
Trapezoid method: 0.001100
Trapezoid method: 0.001083
Trapezoid method: 0.001065
Trapezoid method: 0.001048
Trapezoid method: 0.001031
Trapezoid method: 0.001014
Trapezoid method: 0.000998
Trapezoid method: 0.000981
Trapezoid method: 0.000965
Trapezoid method: 0.000949
Trapezoid method: 0.000933
Trapezoid method: 0.000917
Trapezoid method: 0.000901
Trapezoid method: 0.000886
Trapezoid method: 0.000870
Trapezoid method: 0.000855
Trapezoid method: 0.000840
Trapezoid method: 0.000826
Trapezoid method: 0.000811
Trapezoid method: 0.000797
Trapezoid method: 0.000782
Trapezoid method: 0.000768
Trapezoid method: 0.000755
Trapezoid method: 0.000741
Trapezoid method: 0.000727
Trapezoid method: 0.000714
Trapezoid method: 0.000701
Trapezoid method: 0.000688
Trapezoid method: 0.000675
Trapezoid method: 0.000662
Trapezoid method: 0.000650
Trapezoid method: 0.000638
Trapezoid method: 0.000626
Trapezoid method: 0.000614
Trapezoid method: 0.000602
Trapezoid method: 0.000590
Trapezoid method: 0.000579
Trapezoid method: 0.000567
Trapezoid method: 0.000556
Trapezoid method: 0.000545
Trapezoid method: 0.000535
Trapezoid method: 0.000524
Trapezoid method: 0.000513
Trapezoid method: 0.000503
Trapezoid method: 0.000493
Trapezoid method: 0.000483
Trapezoid method: 0.000473
Trapezoid method: 0.000463
Trapezoid method: 0.000454
Trapezoid method: 0.000444
Trapezoid method: 0.000435
Trapezoid method: 0.000426
Trapezoid method: 0.000417
Trapezoid method: 0.000408
Trapezoid method: 0.000400
Trapezoid method: 0.000391
Trapezoid method: 0.000383
Trapezoid method: 0.000375
Trapezoid method: 0.000367
Trapezoid method: 0.000359
Trapezoid method: 0.000351
Trapezoid method: 0.000343
Trapezoid method: 0.000336
Trapezoid method: 0.000328
Trapezoid method: 0.000321
Trapezoid method: 0.000314
Trapezoid method: 0.000307
Trapezoid method: 0.000300
Trapezoid method: 0.000293
Trapezoid method: 0.000287
Trapezoid method: 0.000280
Trapezoid method: 0.000274
Trapezoid method: 0.000267
Trapezoid method: 0.000261
Trapezoid method: 0.000255
Trapezoid method: 0.000249
Trapezoid method: 0.000243
Trapezoid method: 0.000238
Trapezoid method: 0.000232
Trapezoid method: 0.000227
Trapezoid method: 0.000221
Trapezoid method: 0.000216
Trapezoid method: 0.000211
Trapezoid method: 0.000206
Trapezoid method: 0.000201
Trapezoid method: 0.000196
Trapezoid method: 0.000191
Trapezoid method: 0.000187
Trapezoid method: 0.000182
Trapezoid method: 0.000177
Trapezoid method: 0.000173
Trapezoid method: 0.000169
Trapezoid method: 0.000165
Trapezoid method: 0.000161
Trapezoid method: 0.000156
Trapezoid method: 0.000153
Trapezoid method: 0.000149
Trapezoid method: 0.000145
Trapezoid method: 0.000141
Trapezoid method: 0.000138
Trapezoid method: 0.000134
Trapezoid method: 0.000131
Trapezoid method: 0.000127
Trapezoid method: 0.000124
Trapezoid method: 0.000121
Trapezoid method: 0.000118
Trapezoid method: 0.000114
Trapezoid method: 0.000111
Trapezoid method: 0.000109
Trapezoid method: 0.000106
Trapezoid method: 0.000103
Trapezoid method: 0.000100
Trapezoid method: 0.000097
Trapezoid method: 0.000095
Trapezoid method: 0.000092
Trapezoid method: 0.000090
Trapezoid method: 0.000087
Trapezoid method: 0.000085
Trapezoid method: 0.000083
Trapezoid method: 0.000080
Trapezoid method: 0.000078
Trapezoid method: 0.000076
Trapezoid method: 0.000074
Trapezoid method: 0.000072
Trapezoid method: 0.000070
Trapezoid method: 0.000068
Trapezoid method: 0.000066
Trapezoid method: 0.000064
Trapezoid method: 0.000062
Trapezoid method: 0.000060
Trapezoid method: 0.000059
Trapezoid method: 0.000057
Trapezoid method: 0.000055
Trapezoid method: 0.000054
Trapezoid method: 0.000052
Trapezoid method: 0.000051
Trapezoid method: 0.000049
Trapezoid method: 0.000048
Trapezoid method: 0.000046
Trapezoid method: 0.000045
Trapezoid method: 0.000044
Trapezoid method: 0.000042
Trapezoid method: 0.000041
Trapezoid method: 0.000040
Trapezoid method: 0.000039
Trapezoid method: 0.000038
Trapezoid method: 0.000036
Trapezoid method: 0.000035
Trapezoid method: 0.000034
Trapezoid method: 0.000033
Trapezoid method: 0.000032
Trapezoid method: 0.000031
Trapezoid method: 0.000030
Trapezoid method: 0.000029
Trapezoid method: 0.000028
Trapezoid method: 0.000028
Trapezoid method: 0.000027
Trapezoid method: 0.000026
Trapezoid method: 0.000025
Trapezoid method: 0.000024
Trapezoid method: 0.000023
Trapezoid method: 0.000023
Trapezoid method: 0.000022
Trapezoid method: 0.000021
Trapezoid method: 0.000021
Trapezoid method: 0.000020
Trapezoid method: 0.000019
Trapezoid method: 0.000019
Trapezoid method: 0.000018
Trapezoid method: 0.000018
Trapezoid method: 0.000017
Trapezoid method: 0.000016
Trapezoid method: 0.000016
Trapezoid method: 0.000015
Trapezoid method: 0.000015
Trapezoid method: 0.000014
Trapezoid method: 0.000014
Trapezoid method: 0.000013
Trapezoid method: 0.000013
Trapezoid method: 0.000013
Trapezoid method: 0.000012
Trapezoid method: 0.000012
Trapezoid method: 0.000011
Trapezoid method: 0.000011
Trapezoid method: 0.000011
Trapezoid method: 0.000010
Trapezoid method: 0.000010
Trapezoid method: 0.000010
Trapezoid method: 0.000009
Trapezoid method: 0.000009
Trapezoid method: 0.000009
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000008
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000007
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000006
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000005
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000004
Trapezoid method: 0.000003
Trapezoid method: 0.000003
Trapezoid method: 0.000003
Trapezoid method: 0.000003
Trapezoid method: 0.000003
Trapezoid method: 0.000003
Trapezoid method: 0.000003
Trapezoid method: 0.000003
Trapezoid method: 0.000003
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000002
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000001
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
Trapezoid method: 0.000000
fprintf('Simpson''s composite method: %f\n', norm_simp);
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000001
Simpson's composite method: 0.000002
Simpson's composite method: 0.000002
Simpson's composite method: 0.000002
Simpson's composite method: 0.000002
Simpson's composite method: 0.000002
Simpson's composite method: 0.000002
Simpson's composite method: 0.000002
Simpson's composite method: 0.000002
Simpson's composite method: 0.000002
Simpson's composite method: 0.000002
Simpson's composite method: 0.000002
Simpson's composite method: 0.000002
Simpson's composite method: 0.000002
Simpson's composite method: 0.000003
Simpson's composite method: 0.000003
Simpson's composite method: 0.000003
Simpson's composite method: 0.000003
Simpson's composite method: 0.000003
Simpson's composite method: 0.000003
Simpson's composite method: 0.000003
Simpson's composite method: 0.000003
Simpson's composite method: 0.000003
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000004
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000005
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000006
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000007
Simpson's composite method: 0.000008
Simpson's composite method: 0.000008
Simpson's composite method: 0.000008
Simpson's composite method: 0.000009
Simpson's composite method: 0.000009
Simpson's composite method: 0.000009
Simpson's composite method: 0.000010
Simpson's composite method: 0.000010
Simpson's composite method: 0.000010
Simpson's composite method: 0.000011
Simpson's composite method: 0.000011
Simpson's composite method: 0.000011
Simpson's composite method: 0.000012
Simpson's composite method: 0.000012
Simpson's composite method: 0.000013
Simpson's composite method: 0.000013
Simpson's composite method: 0.000013
Simpson's composite method: 0.000014
Simpson's composite method: 0.000014
Simpson's composite method: 0.000015
Simpson's composite method: 0.000015
Simpson's composite method: 0.000016
Simpson's composite method: 0.000016
Simpson's composite method: 0.000017
Simpson's composite method: 0.000018
Simpson's composite method: 0.000018
Simpson's composite method: 0.000019
Simpson's composite method: 0.000019
Simpson's composite method: 0.000020
Simpson's composite method: 0.000021
Simpson's composite method: 0.000021
Simpson's composite method: 0.000022
Simpson's composite method: 0.000023
Simpson's composite method: 0.000023
Simpson's composite method: 0.000024
Simpson's composite method: 0.000025
Simpson's composite method: 0.000026
Simpson's composite method: 0.000027
Simpson's composite method: 0.000028
Simpson's composite method: 0.000028
Simpson's composite method: 0.000029
Simpson's composite method: 0.000030
Simpson's composite method: 0.000031
Simpson's composite method: 0.000032
Simpson's composite method: 0.000033
Simpson's composite method: 0.000034
Simpson's composite method: 0.000035
Simpson's composite method: 0.000036
Simpson's composite method: 0.000038
Simpson's composite method: 0.000039
Simpson's composite method: 0.000040
Simpson's composite method: 0.000041
Simpson's composite method: 0.000042
Simpson's composite method: 0.000044
Simpson's composite method: 0.000045
Simpson's composite method: 0.000046
Simpson's composite method: 0.000048
Simpson's composite method: 0.000049
Simpson's composite method: 0.000051
Simpson's composite method: 0.000052
Simpson's composite method: 0.000054
Simpson's composite method: 0.000055
Simpson's composite method: 0.000057
Simpson's composite method: 0.000059
Simpson's composite method: 0.000060
Simpson's composite method: 0.000062
Simpson's composite method: 0.000064
Simpson's composite method: 0.000066
Simpson's composite method: 0.000068
Simpson's composite method: 0.000070
Simpson's composite method: 0.000072
Simpson's composite method: 0.000074
Simpson's composite method: 0.000076
Simpson's composite method: 0.000078
Simpson's composite method: 0.000080
Simpson's composite method: 0.000083
Simpson's composite method: 0.000085
Simpson's composite method: 0.000087
Simpson's composite method: 0.000090
Simpson's composite method: 0.000092
Simpson's composite method: 0.000095
Simpson's composite method: 0.000097
Simpson's composite method: 0.000100
Simpson's composite method: 0.000103
Simpson's composite method: 0.000106
Simpson's composite method: 0.000109
Simpson's composite method: 0.000111
Simpson's composite method: 0.000114
Simpson's composite method: 0.000118
Simpson's composite method: 0.000121
Simpson's composite method: 0.000124
Simpson's composite method: 0.000127
Simpson's composite method: 0.000131
Simpson's composite method: 0.000134
Simpson's composite method: 0.000138
Simpson's composite method: 0.000141
Simpson's composite method: 0.000145
Simpson's composite method: 0.000149
Simpson's composite method: 0.000153
Simpson's composite method: 0.000156
Simpson's composite method: 0.000161
Simpson's composite method: 0.000165
Simpson's composite method: 0.000169
Simpson's composite method: 0.000173
Simpson's composite method: 0.000177
Simpson's composite method: 0.000182
Simpson's composite method: 0.000187
Simpson's composite method: 0.000191
Simpson's composite method: 0.000196
Simpson's composite method: 0.000201
Simpson's composite method: 0.000206
Simpson's composite method: 0.000211
Simpson's composite method: 0.000216
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Simpson's composite method: 0.000232
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Simpson's composite method: 0.000321
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Simpson's composite method: 0.000336
Simpson's composite method: 0.000343
Simpson's composite method: 0.000351
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Simpson's composite method: 0.000391
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Simpson's composite method: 0.000426
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Simpson's composite method: 0.000444
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Simpson's composite method: 0.000727
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Simpson's composite method: 0.000782
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Simpson's composite method: 0.000933
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Simpson's composite method: 0.001172
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Simpson's composite method: 0.001228
Simpson's composite method: 0.001247
Simpson's composite method: 0.001266
Simpson's composite method: 0.001285
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Simpson's composite method: 0.001364
Simpson's composite method: 0.001384
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Simpson's composite method: 0.001466
Simpson's composite method: 0.001487
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Simpson's composite method: 0.001572
Simpson's composite method: 0.001593
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Simpson's composite method: 0.001658
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Simpson's composite method: 0.001770
Simpson's composite method: 0.001792
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Simpson's composite method: 0.001861
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Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
Simpson's composite method: 0.000000
fprintf('Exact value: %f\n', norm_exact);
Exact value: 1.000000
% Plot the approximations and the exact values
figure;
subplot(2,1,1);
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1347939/image.png)
length(x)
ans = 2001
length(f_t(x, 10))
ans = 2001
length(x(1:end-1))
ans = 2000
length(t_trap)
ans = 1000
length(x(1:2:end))
ans = 1001
length(t_simp)
ans = 1000
plot(x, f_t(x, 10), 'k', x(1:end-1), t_trap, 'r', x(1:2:end), t_simp, 'b--');
Error using plot
Vectors must be the same length.
Vectors must be the same length.
legend('Exact', 'Trapezoid', 'Simpson''s');
title('T-distribution Probability Density Function');
subplot(2,1,2);
plot(x, f_norm(x), 'k', x(1:end-1), norm_trap, 'r', x(1:2:end), norm_simp, 'b--');
legend('Exact', 'Trapezoid', 'Simpson''s');
title('Normal Distribution Probability Density Function');
2 个评论
Shoaib Salim
2023-4-6
How can i edit to get rid of this error as i tried above mentioned steps but not succeeded
Oguz Kaan Hancioglu
2023-4-7
it is caused by you assigning the same variable name different array.
x = linspace(a, b, n+1); % length of x = 1001
t_trap = h/2 * (f_t(x(1:end-1), 10) + f_t(x(2:end), 10)); % length of t_trap 1001
norm_trap = h/2 * (f_norm(x(1:end-1)) + f_norm(x(2:end)));
% Use Simpson's composite method to approximate the integrals
x = linspace(a, b, 2*n+1); % length of x 2001
% now length of x = 2001 but t_trap = 1001
plot(x, f_t(x, 10), 'k', x(1:end-1), t_trap, 'r', x(1:2:end), t_simp, 'b--');
plesae assign different names for x arrays.
更多回答(1 个)
Joe Vinciguerra
2023-4-6
The x and y vectors for a plot need to be the same length. You were close, but looks like you had a typo. Try this:
% Plot the approximations and the exact values
figure;
subplot(2,1,1);
% plot(x, f_t(x, 10), 'k', x(1:end-1), t_trap, 'r', x(1:2:end), t_simp, 'b--');
plot(x, f_t(x, 10), 'k', x(1:2:end-1), t_trap, 'r', x(1:2:end-1), t_simp, 'b--');
legend('Exact', 'Trapezoid', 'Simpson''s');
title('T-distribution Probability Density Function');
subplot(2,1,2);
% plot(x, f_norm(x), 'k', x(1:end-1), norm_trap, 'r', x(1:2:end), norm_simp, 'b--');
plot(x, f_norm(x), 'k', x(1:2:end-1), norm_trap, 'r', x(1:2:end-1), norm_simp, 'b--');
legend('Exact', 'Trapezoid', 'Simpson''s');
title('Normal Distribution Probability Density Function');
For more details: 2-D line plot - MATLAB plot (mathworks.com)
1 个评论
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