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.

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.

Answer 1

[Torsten]

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