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Math Help - How do you integrate this problem involving trig functions and high exponents?

  1. #1
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    How do you integrate this problem involving trig functions and high exponents?

    I've tried this problem several times and end up with really crazy answers which are too embarrassing to state here. It's:

    ∫ cos(θ) sin(θ)^43 dθ

    I tried with u = sinθ, which I'm not sure is right, and even then I can't integrate the resulting function.
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  2. #2
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    \int {\color{blue}\cos (\theta)} \big[{\color{red}\sin (\theta)}\big]^{43} {\color{blue}\ d \theta}

    You're right! Using your sub we have: {\color{red}u = \sin (\theta)} \ \Rightarrow \ {\color{blue}du = \cos (\theta) \ d\theta }

    Now simply substitute it all in. Can you go on from here?
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  3. #3
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    Thanks! Actually, I don't know where to go from:

    ∫(sin u)^(43) du

    (Sorry I haven't learned the math environment yet.)
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  4. #4
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    No. u is replaced with \sin \theta NOT just \theta

    \int {\color{blue}\cos (\theta)} \big[\underbrace{{\color{red}\sin (\theta)}}_{\displaystyle = \ u}\big]^{43} {\color{blue}\ d \theta}

    So really you should have: \int u^{43} du
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  5. #5
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    Ah! Thank you so much. I have no idea how I could have mistaken that. So it's:

    ∫u^43 du

    u^44 / 44

    (sinθ)^44 / 44
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  6. #6
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    Don't forget the + C !
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