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Homework Help: Fourrier series question.

  1. Nov 22, 2012 #1
    1. The problem statement, all variables and given/known data

    [itex]\ f(x) = e^{|x|}[/itex] with [itex]x \in (-1,1) [/itex] and f(x+2) = f(x) [itex] \forall x [/itex]

    2. Relevant equations

    3. The attempt at a solution

    Linked solution

    What am I meant to do once I get to the last line? (assuming all is right up until then)
    Last edited: Nov 22, 2012
  2. jcsd
  3. Nov 22, 2012 #2


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    Here is that last line.

    $$ 2\int_0^1 e^x \cos(n \pi x)\,dx =
    \frac{2}{n \pi} \left[e^x\sin(n \pi x) \right]_0^1 -
    \frac{2}{n^2 \pi^2} \left[e^x\cos(n \pi x) \right]_0^1 -
    \frac{2}{n^2 \pi^2} \int_0^1 e^x \cos(n \pi x)$$

    Treat that integral as an unknown and solve for it and, of course, put in the evaluated limits.
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