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Doubt with proof of integral of odd function

  1. Jul 4, 2012 #1
    1. The proof
    attachment.php?attachmentid=48872&stc=1&d=1341445316.gif


    2. The doubt

    What I don't understand is when he switch the variable back to x. He says that:
    [tex] \displaystyle \int_{-a}^{0}{f(x)dx=-\int_{0}^{a}{f(x)dx}}[/tex]

    But if we have:
    [tex] \displaystyle \int_{0}^{a}{f(-t)dt=-\int_{0}^{a}{f(t)dt}}[/tex]

    Then if we switch back to x we should have:
    [tex] \displaystyle \int_{-a}^{0}{f(x)dx=\int_{-a}^{0}{f(-x)dx}}[/tex]

    And not what he said. Could you clarify that to me?

    Thanks!
     

    Attached Files:

  2. jcsd
  3. Jul 4, 2012 #2
    I think I got it. I think is a matter of the name of the variable.
     
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