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Calculus 3 Triple Integration in Spherical Coords

  1. Apr 30, 2009 #1
    1. The problem statement, all variables and given/known data

    Use spherical coordinates to evaluate the triple integral z dV where Q is the solid that lies between x^2+y^2+z^2=1 and x^2+y^2+z^2=4.

    2. Relevant equations
    Not sure what goes here :P



    3. The attempt at a solution
    I've gotten everything set up, im having problems with boundaries I think. Currently I am using 0 to 2[tex]\pi[/tex] for [tex]\vartheta[/tex], 0 to [tex]\pi[/tex] for [tex]\varphi[/tex] and 1 to 2 for [tex]\rho[/tex]. When solving, I get zero as my final answer, and since I'm not clear on the conceptual meaning of a triple integral that isn't of a function that equals 1 (volume) I don't know if this answer makes sense.
     
    Last edited: Apr 30, 2009
  2. jcsd
  3. Apr 30, 2009 #2

    Dick

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    It is zero. It's the integral of z on the volume between two spheres centered on the origin. It's as much positive as negative. The two cancel. But you should be using rho from 1 to 2.
     
  4. Apr 30, 2009 #3
    Nevermind, read what you wrote again.
    Thanks for the quick reply!
     
    Last edited: Apr 30, 2009
  5. Apr 30, 2009 #4

    Dick

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    Makes a lot of sense.
     
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