Riley hobson bence · Problem 12.20

Fourier series

Mathematics — Methods · fourier-sine-series-least-squares

Problem

Sketch the graph of the function f(x)f(x), where f(x)={−x(π+x)for −π≤x<0,x(x−π)for 0≤x<π.f(x) = \begin{cases} -x(\pi + x) & \text{for } -\pi \leq x < 0, \\ x(x - \pi) & \text{for } 0 \leq x < \pi. \end{cases} If f(x)f(x) is to be approximated by the first three terms of a Fourier sine series, what values should the coefficients have so as to minimise E3E_3? What is the resulting value of E3E_3?

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