MATLAB: I want use Simpson numerical integration method

integralnumerical integral

I try to integral below function. But it makes some error when I try.
syms x, T, Ef, k
Q = x.^k/(1+exp(-(x-Ef)/T));
int ( Q, x, 0.2, 1);
it makes error they cannot find something.
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Finally, I want to make below function
Function [K] = ff(a,b,c);
k=a; Ef =b, T = c;
Q = x.^k/(1+exp(-(x-Ef)/T));
k = int ( Q, x, 0.2, 1);
Also, if it is possible, numerical integral method is fine for me. I think I can use Simpson numerical integration but please give me some hints to use it.
Thank you!

Best Answer

If you want your integral to be a function of all the parameters, you could define the following:
function y = fintegral(k,Ef,T,lb,ub)
f  = @(x) x.^k./(1+exp(-(x-Ef)/T));
y = quadl ( f, lb, ub);
Then a typical call would look like this:
k = 1; Ef = 2; T = 3; lb = 0.2; ub = 1;
fintegral(k,Ef,T,lb,ub)
 ans =
    0.1884
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