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Math Help - Integration by substitution MkII

  1. #1
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    Integration by substitution MkII

    Here it is

    \int_{0}^{\frac{\pi}{4}} \sin^3(2x)\cos^2(2x)\ where\ the\ sustitution\ is\ u = \cos(2x)

    \frac{du}{dx} = -\frac{1}{2}\sin(2x)

    which means

    -2\sin^2(2x)u^2.du

    I get stuck here
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hello,
    Quote Originally Posted by Beard View Post
    which means

    -2\sin^2(2x)u^2.du

    I get stuck here
    Now you have to find an expression of \sin^2(2x) in terms of u (recall that \sin^2\theta=1-\cos^2\theta).
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  3. #3
    MHF Contributor
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    Just in case it appeals...





    This is only an overview - the lower equality relies on the pythag identity.

    Balloon Calculus: worked examples from past papers
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