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Multiple integration + Centroid Help.

  1. Nov 24, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the volume bounded by sphere rho = rt. 6 and the paraboloid z = x^2 + y^2
    and locate the centroid of this region


    The attempt at a solution

    [​IMG]

    So Thats the integral that I made for this problem, but I'm having trouble integrating it. the rdr throws it off.

    Please Help~! I am having some trouble.
     
  2. jcsd
  3. Nov 24, 2007 #2
    You first integrate with z, that gives you rz in the inside. Using Fubini you get (meaning evaluate the integral) [tex]r\sqrt{6-r^2} - r(r^2)[/tex] and now continue with r and theta.
     
  4. Nov 24, 2007 #3
    So when i evaluate it, I get -12pi rt6 as the answer.
    Am I doing it wrong? I feel like im not doing right. If you could, could I see how someone would do a problem like this? Evaluating integrals is a little confusing for me.

    And then I need lots of help on the centroid part as well. Thanks~
     
  5. Nov 25, 2007 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Why don't you show us what you did and we can comment on it.
     
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