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Math Help - Line Integral Problem

  1. #1
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    Line Integral Problem

    I have this problem:

    Evaluate the line integral, where C is the given curve.
    ∫C xyz ds
    C: x = 9sin(t), y = t, z = -9cos(t), 0 ≤ tπ

    After applying the parametrization and everything, I ended up with having to integrate something like: t*sin(t)*cos(t)dt

    I have no clue how to integrate that. Integration by parts fails as far as I see, and I can't think of any identities or other tricks to change it to something workable.
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  2. #2
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    Quote Originally Posted by Joshai View Post
    I have this problem:

    Evaluate the line integral, where C is the given curve.
    ∫C xyz ds
    C: x = 9sin(t), y = t, z = -9cos(t), 0 ≤ tπ

    After applying the parametrization and everything, I ended up with having to integrate something like: t*sin(t)*cos(t)dt

    I have no clue how to integrate that. Integration by parts fails as far as I see, and I can't think of any identities or other tricks to change it to something workable.
    Note that t \sin t \cos t = \frac{1}{2} t \sin (2t) via the usual double angle formula. Now use integration by parts.
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