Compute the Fourier series of f(x)=x+|x|,-π≤x≤π

Answer 1

well, you have to break f(x) into two parts

for x<0, f(x) = 0
for x >= 0, f(x) = 2x

so,
a0 = 1/π ∫[0,π] 2x dx = π

and for the others just use integration by parts for integrals of x cos(nx), etc.

Answer 2

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