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Math Help - Trig Integral Identity

  1. #1
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    Trig Integral Identity

    Hi I'm doing a dynamics problem, To get it into the form wanted I've reduced the problem to showing that
    <br />
\int_{0}^{\pi/2} cos^2 x sin^8 x dx = \frac{1}{9} \int_{0}^{\pi/2} cos^{10} x dx<br />

    Apologies, the above latex code renders fine on my machine but it looks like the forum doesn't support it

    It's meant to say
    \int_{0}^{\pi/2} \cos^2 x \sin^8 x dx = \frac{1}{9} \int_{0}^{\pi/2} \cos^{10} x dx

    Is there any obvious quick way of doing this, or a hint would be nice, I've thought of integrating it by parts but I cant quite see a nice way of splitting it.
    Last edited by mr fantastic; June 7th 2011 at 04:08 PM. Reason: Restored deleted question.
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  2. #2
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    Use parts: u=\cos(x)~\&~dv=\cos(x)\sin^8(x)
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