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Homework Help: Very quick triple integral question

  1. May 5, 2010 #1
    1. The problem statement, all variables and given/known data
    Use the Divergence Theorme to evaluate the flux of v(x,y,z)=[tex]x^{2}[/tex]i+[tex]y^{2}[/tex]j+[tex]z^{2}[/tex]k on the solid T bounded above by a sphere with radius 3 and below by the xy-plane.
    I've found that div(v) is 2(x+y+z).

    When I go to set up the integral I get a triple integral over T of (x+y+z)dV (and I bring the 2 outside the integral). So, of course, I switch to spherical coordinates.
    Now, my question. When I do the switch, can I treat (x+y+z) as sqrt(r), or do I actually have to plug in the parametrized x, y, and z and evaluate?

    Thanks.
     
  2. jcsd
  3. May 5, 2010 #2

    tiny-tim

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    hi narfarnst! :smile:

    (have a square-root: √ :wink:)
    but it isn't √r ! :rolleyes:

    so, yes, you do actually have to do the work! :smile:
     
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