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Fourier Coefficients for asymmetric interval

  1. Jan 22, 2012 #1
    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. jcsd
  3. Jan 22, 2012 #2

    Dick

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    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?
     
  4. Jan 22, 2012 #3
    oh right thank you.
    and yea that should be sin(kx) for bk my bad.
     
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