6Chapter 2Fourier SeriesSolutions to Exercises 2.21.The graph of the Fourier series is identical to the graph of the function, exceptat the points of discontinuity where the Fourier series is equal to the average of thefunction at these points, which is12.5.We compute the Fourier coefficients using he Euler formulas. Let us first notethat sincef(x) =|x|is an even function on the interval-π<x<π, the productf(x) sinnxis an odd function. Sobn=1ππ-πodd function|x|sinnx dx= 0,because the integral of an odd function over a symmetric interval is 0. For the othercoefficients, we havea0=12ππ-πf(x)dx=12ππ-π|x|dx
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