Boole's Approximation

Question

Syed Abdul Rafay 2022-11-24

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链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1861623-boole-s-approximation

评论： Image Analyst 2022-11-24

I checked my code several times but I can not find the mistake. There is a huge difference between the exact answer and Boole's approximate value.

function Boole_approx(a,b)
a = -1;
b = 1;
N=10; %total number of intervals
h = (b-a)/(4*N); %shows the steps increment
x = a:h:b;
s=((2*h)/45)*(7*(f(a)+f(b)));
for i=1:2:N-1
    s = s + ((2*h)/45)*(32*f(x(i)));
end
for i=2:4:N-2
    s = s + ((2*h)/45)*(12*f(x(i)));
end
for i=4:4:N-4
    s = s + ((2*h)/45)*(14*f(x(i)));
end
disp (s)
G = @(x)(tan(x)-2.*x);
exact_value = integral(G,0,pi)
end
function fx=f(x)
fx = tan(x)-2*x;
end

Answer

resuts =

0.232772096457974 -9.87116269500961

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Image Analyst 2022-11-24

What did you pass in for a and b?

And why do you immediately ovrewrite them with -1 and 1, thus making the input arguments totally irrelevant?

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Answer 1

Alan Stevens 2022-11-24

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1861623-boole-s-approximation#answer_1110773

You are using Boole from -1 to 1, but the "exact" from 0 to pi. (You should plot G against x to see why your "exact" integral won't produce a sensible numerical answer).

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Syed Abdul Rafay 2022-11-24

sorry I made a mistake her but it is to pi in original code. I forgot to correct it while pasting. I tried 5 to 6 time inf is the answer of boole's and 67 for exact

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