Calculating fourier coefficients

[gravenewworld]

I need to find the Fourier series for the function f(x)=x. I have come across trying to find the integral from -pi to pi of -ixSin(nx). How do I go about evaluating this integral when n is infinity? I seem to only be able to find integrals in an integral table where n is an integer, but not when n could be infinity.

 

[Galileo]

Why in the world would you want to put infinity in the argument? It doesn't even mean anything.
You can calculate any Fourier coefficient you need, what more could you ask for?

 

[gravenewworld]

Why in the world would you want to put infinity in the argument?

Maybe I am misunderstanding something here. But the Fourier series definition I have for f(x) is Sum from n=-infinity to positive infinity of (f(x),en)en where en is the complete orthonormal seqeunce (2pi)^-1/2 *e^inx and the inner product ( , ) is for the hilbert space L^2(-pi, pi). So when n is +/- infinity how would I go about calculating the inner product for L^2?

 

[HallsofIvy]

Yes, you are misunderstanding! Saying that n "goes from -infinity to infinity" means that n takes on all integer values. n is never "infinity" because n is an integer and "infinity" is not even a real number, much less an integer.