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Math Help - variable sustitution

  1. #1
    Newbie nigromante's Avatar
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    variable sustitution

    Someone knows how to demostrate

    Integral (senxcosx)^m, {0,Pi/2}=2^m·Integral(cosx)^m, {0,Pi/2}???

    Thanks by hand
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  2. #2
    MHF Contributor
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    Re: variable sustitution

    Hey nigromante.

    Is your senx sin(x), or sec(x), (or something else)?
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  3. #3
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    Re: variable sustitution

    It's sin(x). The Spanish (and Italian) word for sine is seno, so they use sen(x) instead of sin(x).

    Here's a start:

    \int_0^{\frac{\pi}{2}}(\sin{x}\cos{x})^m\ dx=2^{-m}\int_0^{\frac{\pi}{2}}(\sin{2x})^m\ dx

    which uses the identity \sin{2u}=2\sin{u}\cos{u}. It looks like you might want to use the identity \sin{u}=\cos{\left(\frac{\pi}{2}-u\right)}. I'm pretty sure you'll need to have 2^{-m} instead of 2^m.


    - Hollywood
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  4. #4
    Newbie nigromante's Avatar
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    Re: variable sustitution

    Thanks for your answers, Holliwood is right, I'm mexican, and is again right, I need 2^-m. Thanks again to all.
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