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Math Help - Help with a triple Integration Question?

  1. #1
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    Help with a triple Integration Question?

    Hi I am having difficulty with the following question

    2. Using cylindrical polar co-ordinates r, theta , z, evaluate
    ∫∫∫B z^7 dV; where B is the finite body between the plane z = 0 and the paraboloidal surface S : z = 36 − x^2 − y^2.

    I have managed to find the limit of theta which is 2pi and 0, but I am struggling to find it for r and z. For z I think one of the limits is 36-r^2 and the other limit for z is 0 (do you think this is right), also what would the limits of r be ( would it be 6 and -6 or 6 and 0)
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  2. #2
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    Re: Help with a triple Integration Question?

    In cylindrical coordinates, which is what what the problem specifically asks you to use, the paraboloidal surface is z= 36- r^2. It should be easy to see that z is never more than 36. And you are told that z is not below 0. For each z, r goes from 0 to r= \sqrt{36}= 6. Or you could argue that r goes from 0 to a largest value of 6 (where z= 0) and, for each r, z goes from 0 to 36- r^2.
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  3. #3
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    Re: Help with a triple Integration Question?

    Quote Originally Posted by HallsofIvy View Post
    In cylindrical coordinates, which is what what the problem specifically asks you to use, the paraboloidal surface is z= 36- r^2. It should be easy to see that z is never more than 36. And you are told that z is not below 0. For each z, r goes from 0 to r= \sqrt{36}= 6. Or you could argue that r goes from 0 to a largest value of 6 (where z= 0) and, for each r, z goes from 0 to 36- r^2.
    Thanks - for the theta limits I thought it was 2pi to 0 but now I think it might be pi/2 to 0, what do you think?
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