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Math Help - Periodic Functions and Fourier Series

  1. #1
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    Periodic Functions and Fourier Series

    Here's a question I can't figure out =[

    Suppose f(x) is a 2L-periodic function: f(x+2L) = f(x). Show:

    \int_{-L}^{L} f(x) dx = \int_{a}^{a+2L} f(x) dx

    for any value of a.
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  2. #2
    Super Member Aryth's Avatar
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    You just need to show that the integral yields the same value when the period is used as the interval. You can see that [-L,L] is 2L in length, and then [a, a+2L] is also 2L in length, and since f(x) is a 2L periodic function, then it is the same over all periods, regardless of the starting point.
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