Question

Find the Fourier series for f(x) = x - x? in the interval [-π,π]​

Answer 1

Step-by-step explanation:

I am totally new to Fourier series. Here I try to compute the Fourier series for the function f(x)=xf(x)=x over the interval −π≤x≤π−π≤x≤π.

Since f(x)f(x) is an odd function:

an=0an=0 (why is this the case?),

bn = 1π∫π−πf(x)sin(nx)dx = 1π∫π−πxsin(nx)dx

bn = 1π∫−ππf(x)sin⁡(nx)dx = 1π∫−ππxsin⁡(nx)dx

.

Which means

−xcos(nx)n+sin(nx)n2