Fourier Expansion for a One-Period Function with Period 2pi

[Kuma]

Homework Statement

Given this one period graph of a function with period 2pi,

find a Fourier expansion.

Homework Equations

The Attempt at a Solution

So I was wondering if i can split up the integrals into two parts to find the coefficients. It is an even function so ak = 0.

for bk can I split the integral as follows

1/pi[int 0 to pi (x cos kx dx) + int pi to 2pi ((-x+2pi) cos kx dx]

?

 

[vela]

Yup, that's what you're supposed to do. Also, remember a₀ isn't equal to 0.