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Math Help - Fouries series integration help

  1. #1
    Junior Member
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    Fouries series integration help

    Hey everyone, I am stuck on 2 questions, so if anyone can help me that would be much appreciated.

    f(x)=\begin{Bmatrix} 2, & -1<x<1\\0, & 1<|x|<2\end{matrix}

    Fourier Series representation:
    f(x)=a_0 + \sum_{n=1}^{\infty}(a_n \cos(\frac{n \pi x}{2}) +b_n \sin(\frac{n \pi x}{2}))

    The first question is to integrate both sides of f(x) from -2 to 2 to show that a_0=1.
    The second question is to multiply both sides of f(x) by sin(\frac{m \pi x}{2}) and integrate from -2 to 2 to show that b_n=0.

    Because of the domain restrictions on f(x) I can't figure out what to do for these questions.

    If you can help me it would be nice. Thanks
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  2. #2
    Senior Member
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    Integrating F equation
    \int_{-2}^2 f(x) \; dx=\int_{-2}^2 a_0 \; dx
    May be shown that other terms are zeros.
    \int_{-2}^2 f(x) \; dx=\int_{-1}^1 2 \; dx=4
    \int_{-2}^2 a_0 \; dx=4a_0
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  3. #3
    Junior Member
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    Thanks zzzoak, I get question 1, but I still don't understand how to do the 2nd question.
    Last edited by Nguyen; September 22nd 2010 at 08:24 PM.
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