MathCastle
Differential EquationsMediumBoundary Values & Fourier Series

Boundary Values & Fourier Series · Medium problem

Let f(x)=0f(x) = 0 for −π<x<0-\pi < x < 0 and f(x)=xf(x) = x for 0<x<π0 < x < \pi. Find its Fourier coefficient a1=1π∫−ππf(x)cos⁡x dxa_1 = \dfrac1\pi\displaystyle\int_{-\pi}^{\pi} f(x)\cos x\,dx.