n 2-2) Let , (x) = sin ,,x, with eigenvalues ,,= n/L, for n = 1,...

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n 2-2) Let , (x) = sin ,,x, with eigenvalues ,,= n/L, for n = 1, 2, 3 ... over the interval 0 x L, noting that the weighting function is 1. a. Show that the integral f(x)m (x) dx = 0 for n m. b. Evaluate the norm of the eigenfunction, namely, fo[n(x)] dx. c. Determine the general Fourier series expansion coefficients (C) for the following, simplifying all integrals as much as possible. =C C, sin(x,x) n=1 4x = n 2-2) Let , (x) = sin ,,x, with eigenvalues ,,= n/L, for n = 1, 2, 3 ... over the interval 0 x L, noting that the weighting function is 1. a. Show that the integral f(x)m (x) dx = 0 for n m. b. Evaluate the norm of the eigenfunction, namely, fo[n(x)] dx. c. Determine the general Fourier series expansion coefficients (C) for the following, simplifying all integrals as much as possible. =C C, sin(x,x) n=1 4x =

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a To show that the integral of xmxdx is 0 for n m we need to evaluate the integral over the interval ... View the full answer