# Fourier Coefficients for asymmetric interval

1. Jan 22, 2012

### mottov2

1. The problem statement, all variables and given/known data
Fidn the Fourier expansion for f of period 2Pi that corresponds to y=x/3 on the interval [0,2Pi)

Im just a little confused about if im setting up the integration properly. The asymmetric interval is kind of confusing me here.
3. The attempt at a solution
a0 = 1/Pi ∫ x/3 dx = 0 (since f is odd) for 0 < x < 2Pi.

ak = 1/Pi ∫ x/3 Cos(kx) dx = 0 (since f is odd) for 0< x < 2Pi

bk = 1/Pi ∫ x/3 Sin(kx) dx for 0 < x < 2Pi

Last edited: Jan 22, 2012
2. Jan 22, 2012

### Dick

Since the interval isn't symmetric you can't use the trick that the integral of an odd function is zero. Both the a's and the b's may be nonzero. And that should be a factor Sin(kx) in the b integral, right?

3. Jan 22, 2012

### mottov2

oh right thank you.
and yea that should be sin(kx) for bk my bad.