91Ó°ÊÓ

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

Find the Fourier series for the given function \(f\) $$ f(x)=x^{3} \quad \text { for } x \in I=\\{x:-\pi \leqslant x \leqslant \pi\\} $$

Find the Fourier series for the given function \(f\) $$ f(x)=e^{2 x} \quad \text { for } x \in I=\\{x:-\pi \leqslant x \leqslant \pi\\} $$

Given the function \(f: x \rightarrow x|x|\) for \(x \in I=\\{x:-\pi

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

Find the Fourier series for the given function \(f\) $$ f(x)=\sin ^{2} x \quad \text { for } x \in I=\\{x:-\pi \leqslant x \leqslant \pi\\} $$

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

Find the Fourier series of the function \(f\) on the interval \(I=\\{x:-L

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

Find the Fourier series of the function \(f\) on the interval \(I=\\{x:-L