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Math Help - Definite integral

  1. #1
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    Definite integral

    Proof, without calculation, that:

    \int^\pi_{-\pi}(4arctane^x-\pi) dx = 0

    I was thinking to show that the integrand is an odd function and then, since the interval is symmetrical, it means that the definite integral is zero. But how do I show that 4arctane^x-\pi is an odd function?
    Last edited by loui1410; June 12th 2012 at 12:24 PM.
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  2. #2
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    Re: Definite integral

    Use the fact that the derivative of an odd function is even (and that the reverse implication also is true under certain conditions). Derive the integrand and see if you can conclude that the derivative indeed is even.
    Last edited by thesmurfmaster; June 12th 2012 at 12:41 PM.
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  3. #3
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    Re: Definite integral

    What are the "certain conditions"?
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  4. #4
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    Re: Definite integral

    Integrate f'(x) = f'(-x) and see what you come up with.
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