91Ó°ÊÓ

Find the Fourier series for the given function \(f\) $$ f(x)= \begin{cases}0 & \text { for } x \in I_{1}=\\{x:-\pi \leqslant x<\pi / 2\\} \\ 1 & \text { for } x \in I_{2}=\\{x: \pi / 2 \leqslant x \leqslant \pi\\}\end{cases} $$

Find the Fourier series for the given function \(f\) $$ f(x)= \begin{cases}0 & \text { for } x \in I_{1}=\\{x:-\pi \leqslant x<0\\} \\\ x & \text { for } x \in I_{2}=\\{x: 0 \leqslant x \leqslant \pi\\} .\end{cases} $$

Find the Fourier series for the given function \(f\) $$ f(x)=|\cos x| \quad \text { for } x \in I=\\{x:-\pi \leqslant x \leqslant \pi\\} $$

Find the Fourier series for \(f\) given by $$ f: x \rightarrow \begin{cases}-(\pi+x) & \text { for } I_{1}=\left\\{x:-\pi \leqslant x \leqslant-\frac{1}{2} \pi\right\\} \\ x & \text { for } I_{2}=\left\\{x:-\frac{1}{2} \pi \leqslant x \leqslant \frac{1}{2} \pi\right\\} \\ \pi-x & \text { for } I_{3}=\left\\{x: \frac{1}{2} \pi \leqslant x \leqslant \pi\right\\}\end{cases} $$