Optimize the construction of a function for quadrature purposes

Hello,

I want to compute the integral of a function which is the linear combination of some known function family (here, Fourier functions):

MyInt = integral(@(t) myfun(t), 0, 2*pi);

My function myfun(t) is built as follows:

function Output = myfun(t)
Output = 0;
for p = 1:20
    Output = Output + 1/p.*cos(p*t);
    Output = Output + 1/(2*p).*sin(p*t);
end

I can't think of a way to vectorize what's above without the for loop? Can we do better?

Thank you

Answer 1

[Torsten]

MyInt = integral(@myfun, 0, 2*pi)

MyInt = -5.5511e-16

function Output = myfun(t)
  p = (1:20).';
  Output = sum(1./p.*cos(p.*t) + 1./(2*p).*sin(p.*t),1);
end