Determine a série de Fourier de f no intervalo indicado. f(x)=\left\{\begin{array}{lr}0, & -\pi<x<0 \\\ \operatorname{sen} x, & 0 \leq x<\pi\end{array}\right.
Usando \operatorname{sen} x\cos(nx)=\tfrac12\bigl[\operatorname{sen}((n+1)x)+\operatorname{sen}((1-n)x)\bigr] e sabendo que \int_{0}^{\pi}\operatorname{sen}(kx)\,dx=\tfrac{1-(-1)^k}{k}, obtemos após simplificar