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Evaluate the Flux with Divergence Theorem

  1. Dec 10, 2013 #1
    1. The problem statement, all variables and given/known data
    Evaluate the flux where F = <(e^z^2,2y+sin(x^2z),4z+(x^2+9y^2)^(1/2)> in the boundary of the region x^2 + y^2 < z < 8-x^2-y^2

    2. Relevant equations

    3. The attempt at a solution
    So using the divergence Theorem,

    ∇ dot F = 6

    ∫∫∫6r dzdrdθ

    where z is bounded between r^2 and 8-r^2
    and r is bounded between 0 and 8^(1/2)
    and θ is bounded between 0 and 2∏

    is this correct?
    I'm mainly worried about my limits of integration for r and z are incorrect, can anyone verify?
  2. jcsd
  3. Dec 10, 2013 #2
    Okay so yeah what I wrote is probably wrong, can anyone help me and my friends along?
  4. Dec 10, 2013 #3
    I just realized that the r bound should go from 0 to 2? right??
  5. Dec 11, 2013 #4


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    Gold Member

    The enclosed volume is the volume between two paraboloids. I think what you have is correct.
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