I tried to create a mid point formula and trapezoid formula in Matlab and solve a integral using it but I'm not getting the same result as the build in function.

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Mingxuan
Mingxuan 2022-10-16
编辑： Torsten 2022-10-17
Ran in:
we are trying to use these two formula to approximate a integral value. instead of using the build in function of
format long
integral(@(x)exp(-x.^4),0,20)
ans =
0.906402477055477
but the result should match the result of build in function.
we are trying to approxiamte this integral
my code is follows
a = 0;
b = 20;
n = 10000;
h = (b-a)/n;
x = linspace(a,b,n+1);
y = exp(-x.^4);
x_mid = a+h/2:h:b;
t_form = h*(sum(y)+((y(1)+y(end))/2))
t_form =
0.908402477055477
my result doesn't match the original result. But i'm not sure where the problem is.

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采纳的回答

Torsten
Torsten 2022-10-16
编辑：Torsten 2022-10-17
Ran in:
a = 0;
b = 20;
h = 1e-2;
x = a:h:b;
y = exp(-x.^4);
x_mid = a+h/2:h:b-h/2;
y_mid = exp(-x_mid.^4);
format long
trapz_form = h*((y(1)+y(end))/2+sum(y(2:end-1)))
trapz_form =
0.906402477055477
mid_point_form = h*sum(y_mid)
mid_point_form =
0.906402477055477
reference_int = integral(@(x)exp(-x.^4),0,20)
reference_int =
0.906402477055477

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