Fourier Coefficients for asymmetric interval

[mottov2]

Homework Statement

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 I am setting up the integration properly. The asymmetric interval is kind of confusing me here.

The Attempt at a Solution

a₀ = 1/Pi ∫ x/3 dx = 0 (since f is odd) for 0 < x < 2Pi.

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

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

 

[Dick]

Homework Statement

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 I am setting up the integration properly. The asymmetric interval is kind of confusing me here.

The Attempt at a Solution

a₀ = 1/Pi ∫ x/3 dx = 0 (since f is odd) for 0 < x < 2Pi.

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

b_k = 1/Pi ∫ x/3 Cos(kx) dx for 0 < x < 2Pi

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?

 

[mottov2]

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