Integration approximation with function handle

Hi, i am having issues with a problem at school.

The assignment is to approximate an integral by(as i understand) looping a function for a set number of times.

Also this function needs to be called upon by a separate script.

I can't get my head around the problem so any help would be gratefully accepted.

The problem:

"" Design a function that approximates integrals with the following formula:

Where h = (b-a)/h. The input parameters must be, a, b, n and an anonymous function (a handle) for f

The only built-in features that can be used are linspace and sum.

Also design a script that calls the function and uses the call to calculate the error

i.e. the (nearest value -the exact value) if a = pi/ 2, b=pi, n=15 and f(x) = xsinx.

The exact the value must be calculated by yourself with partial integration. ""

I have done the hand calculations which results in pi-1

Code1:

I=integralapprox(pi/2,pi,15,@(x) x*sin(x));
E = pi-1;
S = I-E;

Code2:

function I=integralapprox(a,b,n,f0)
h = (b-a)/n;
f = @(a,b,h,f0) ((a+(n-1)*h+a+n*h)/2)*f0;
N=0;
for n=1:n
    F = f(a,h,n,f0);
    N = N + S;
end
I=h*N;

[Torsten]

The formula you use to approximate the integral is wrong.

Answer 1

[Jan]

f = @(a,b,h,f0) ((a+(n-1)*h+a+n*h)/2)*f0;

This cannot work if f0 is a function handle.

This is at least confusing:

for n=1:n    

Start to write the sum again:

function S = integralapprox(a, b, n, f)
 h = (b - a) / n;
 S = 0;
 for k = 1:n
     S = S + f(???);  % Use k as index, not n
 end
 S = h * S;
end