How do I call and multiply handles from an array in integral or quad function?

Hello. For my homework I'm trying to approximate a function with Least squares method, but I face a problem with the function quad(integral). I would like to integrate multiplied elements from B (which are actually handle functions). I have an array of functions:

B= @(x) [1, sin(x), cos(x),sin(x).*cos(x)]; %base functions

and I would like to make a matrix A of integrated multiplied functions. So I have to get 4x4 matrix with integrals of multiplied functions such as : in the first column I would like to have integrals of 1*1, 1*sin(x), 1*cos(x), 1*sin(x)*cos(x); in the second column integrals of sin(x)*1, sin(x)*sin(x), sin(x)*cos(x), sin(x)*cos(x)*sin(x) etc.

My problem is that functions QUAD or INTEGRAL are returning me errors. I have tried everything I found around the internet but no success.

Here is my code:

function ap = MNK(n)

B= @(x) [1, sin(x), cos(x),sin(x).*cos(x)];
A=zeros(n,n);

%f = @x exp(x(x+1))

for i=1:n

      for j=1:n  

        A(i,j) = integral(@(x)B(i)*B(j),-1,1); %problem

      end

      %b(i)=quad(@x B(i).*f(x),-1,1,1e-12); %second part, same problem (just the second function is not base function but our function f)

    end

end

So my question is: How do I call and multiply handles from array B in my integral(or quad) function. Please, I could use any help, because I'm stuck for 2 days now.

Answer 1

[Andrew Newell]

You can replace B by a cell array of functions, and then call the functions when it's time to integrate:

Bfuns = {@(x) ones(size(x)), @sin, @cos, @(x)sin(x).*cos(x)};
%f = @x exp(x(x+1))

A=zeros(n,n);
for i=1:n
    for j=1:n  
      A(i,j) = integral(@(x) Bfuns{i}(x).*Bfuns{j}(x),-1,1); %problem
    end
    %b(i)=quad(@x B(i).*f(x),-1,1,1e-12); %second part, same problem (just the second function is not base function but our function f)
end

Note that I had to use ones(size(x)) to make sure it outputs a vector of the appropriate size. I didn't include the function statement because I don't know how ap is related to A and b.