MATLAB: Error for an usual integration code

numerical integration

Hi, I actually do not understand what I have done wrong, but the code just gives out an error all the time.

function s=integrate(f,a,b,n)
x=0:(n-1);
h=(b-a)/n;
x=a+h*x;
s=0;
for i=1:n
    s=s+f(x(i))*h;
end
end

For integrate(1,2,3,4) i get the error

Index exceeds the number of array elements (1).

Error in integrate (line 7)

s=s+f(x(i))*h;'

and for f=sin(x)

'Undefined function or variable 'x'.

You probably need to pass @sin or @(x) sin(x) and you are probably instead passing sin(x) without any @

integral = simpsonsrule(@(x) (1-x.^3)*sin(x) + exp(x.^2/20),-1,4,20)

You need the @(x) to make an anonymous function

The upper limits in the first two for-loops are not right. They should be:

for i = 1:3:n-2
  x(i) = a + h*i;
  S = S + 3*feval(f, x(i));
end
for i = 2:3:n-1
  x(i) = a + h*i;
  S = S + 3*feval(f, x(i));
end

Your second for-loop: "for i = 2:3:n-2" incorrectly leaves out the term with 3*feval(f,x(n-1)).