Find the fourier series of f on the given interval. f(x) = 1, ? 7 < x < 0 1 + x, 0 ? x < 7

The Fourier series expansion of is given by



where we have





The coefficients of the cosine series are






When is even, the numerator vanishes, so we consider odd , i.e. for , leaving us with



Meanwhile, the coefficients of the sine series are given by






So the Fourier series expansion for is