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Odd, periodic functions

  1. Sep 18, 2008 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    Can you confirm these statements:

    1) If I integrate an odd, periodic function of period 2L over one period, then the integral equals zero.

    2) If I have a function f(x) with period 2L, then f(x+alfa), where alfa is an arbitrary number, will not change it's period.

    Thanks in advance.

    Best regards,
    Niles.
     
  2. jcsd
  3. Sep 18, 2008 #2

    tiny-tim

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    Hi Niles! :smile:

    (have an alpha: α :smile:)

    Hint: prove 2) first (use the obvious substitution) … then use that result to prove 1). :wink:
     
  4. Sep 18, 2008 #3
    Thanks for the α.

    Hmm, well, does #2 really need any proof? I mean, isn't it kinda obvious? Adding a constant α will just translate the function on x-axis (either to the left or right), so the period will remain unchanged.

    And for #1: I can't see the link between this and the previous question.

    Best regards,
    Niles.
     
  5. Sep 18, 2008 #4

    tiny-tim

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    oops!

    Hi Niles! :smile:
    oops!

    I misread 2) as ending "will not change its integral" :redface:

    Prove that, and then prove 1).

    Sorry! :smile:
     
  6. Sep 18, 2008 #5
    I have proven that the definite integral of a 2L-periodic function is the same over any interval of length 2L.

    But I still can't see what the link is between this proof/theorem and my question #1.
     
  7. Sep 18, 2008 #6
    Ok, I got it now.. you were right.

    Thanks!
     
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