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Thread: Help triple integral

  1. #1
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    Help triple integral

    Hi,
    I've tried to solve this integral using cylindric coordinates but it seems very difficult.
    Any help is welcome.


    Help triple integral-integral.jpg
    Attached Thumbnails Attached Thumbnails Help triple integral-integral.jpg  
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  2. #2
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    Re: Help triple integral

    First, a comment

    there are no values of $z$ for which

    $\left(\frac{1}{2},\frac{1}{3},z\right)$

    is in $\Omega $

    once that is fixed it shouldn't be difficult to set up the integral in cylindrical coordinates
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  3. #3
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    Re: Help triple integral

    I tried this
    Help triple integral-20181227_212556.jpg

    Help triple integral-20181227_212521.jpg
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  4. #4
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    Re: Help triple integral

    Looks OK

    for the evaluation of the integral it may be easier to write

    $\displaystyle \sin \theta \sqrt{\sin ^2\theta -\cos ^2\theta }=\sin \theta \sqrt{1-2\cos ^2\theta }$
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  5. #5
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    Re: Help triple integral

    Quote Originally Posted by Idea View Post
    Looks OK

    for the evaluation of the integral it may be easier to write

    $\displaystyle \sin \theta \sqrt{\sin ^2\theta -\cos ^2\theta }=\sin \theta \sqrt{1-2\cos ^2\theta }$
    Ok I try
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  6. #6
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    Re: Help triple integral

    Solved. Thank you
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