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Differential EquationsEasyBoundary Values & Fourier Series

Boundary Values & Fourier Series · Easy problem

Let f(x)=0f(x) = 0 for −1<x<0-1 < x < 0 and f(x)=1f(x) = 1 for 0<x<10 < x < 1. In its Fourier series on [−1,1][-1, 1], bn=∫−11f(x)sin⁡(nπx) dxb_n = \displaystyle\int_{-1}^{1} f(x)\sin(n\pi x)\,dx. Find b1b_1.