I am trying to find the Fourier series, using integration and known knowledge of the Fourier Series, of:
$$f(x)= x, \quad 0<x<\pi$$
I know the $f(x)= x$ is an odd function and so I believe that $a_n = 0$.
I then worked through to find $b_n$ using:
$$b_n=\displaystyle{\frac{1}{L}\int_{-L}^{L}f(x) \sin \frac {nx\pi}{L} dx}$$
But when I finally put everything together I didn't end up getting what I wanted. I know that for $0<x<\pi$ that I will end up with a partial sawtooth wave, however, I just can't get it.
Any help would be appreciated. Also sorry for the formatting if it is wrong, I can never seem to get that as well.