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Math Help - Triple-angle formulae in integration

  1. #1
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    Triple-angle formulae in integration

    ∫sin^2(3x) dx
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  2. #2
    MHF Contributor red_dog's Avatar
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    \int\sin^23xdx=\int\frac{1-\cos 6x}{2}dx=\frac{1}{2}\int dx-\frac{1}{2}\int\cos 6xdx=\frac{x}{2}-\frac{\sin 6x}{12}+C
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  3. #3
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    I dont understand:

    \int\sin^23xdx=\int\frac{1-\cos 6x}{2}dx

    more detail please
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  4. #4
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    Quote Originally Posted by gamboo View Post
    I dont understand:

    \int\sin^23xdx=\int\frac{1-\cos 6x}{2}dx

    more detail please
    power reduction identity ...

    \sin^2{u} = \frac{1 - \cos(2u)}{2}

    derived from the double angle identity for cosine ...

    \cos(2u) = 1 - 2\sin^2{u}<br />
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  5. #5
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    Thanks to both of you.
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