How to find Fourier sine series of $f(x)=x(1-x), 0\lt x \lt 1$?

Question

How to find Fourier sine series of $f(x)=x(1-x), 0\lt x \lt 1$?

This is not an odd functions, so how to proceed?

Answer 1

Define $g(x)=f(x)$ where $0<x<1$ and $g(x)=-f(-x)$ for $-1<x<0$. Then $g$ is an odd function. So you have to expand $g$ and that's the same as expanding $f$ in a sin series.