1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    http://www.mathhelpforum.com/math-help/latex2/img/4deb41286077aabd94b30802f0e6a68a-1.gif [Broken]

    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.
    Last edited by a moderator: May 3, 2017
  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


    User Avatar
    Science Advisor

    Why don't you show us what you did and we can comment on it.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook