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Math Help - [SOLVED] Cylindrical Coordinate Volume Integration

  1. #1
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    [SOLVED] Cylindrical Coordinate Volume Integration

    9. Use polar coordinates to compute the volume of the region defined by 4 - x^2 - y^2 less or equal to z less than or equal to 10 - 4x^2 - 4y^2.

    answer in book: 6pi
    my answer: 2pi

    I got the root of 2 by setting the equations that bound z equal to eachother. It resulted in an equation for a circle equal to two. And to get the area of a circle, you have to do all 360 degrees, so I used 2pi. What's going wrong here?
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  2. #2
    MHF Contributor arbolis's Avatar
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    In the triple integral, you have functions of x and y as upper limits. You have to translate them into polar coordinates.
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  3. #3
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    Quote Originally Posted by arbolis View Post
    In the triple integral, you have functions of x and y as upper limits. You have to translate them into polar coordinates.
    You can translate them before you put them in the limits for Z or after you've calculated the integral for Z. But while I checked your method through with mental math, I came across my rather awful error. I basically said -4r^2 -(-r^2) = -5r^2. But it should obviously equal -3r^2.

    Problem solved. No one waste any more time here!
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