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Homework Help: Volume integral, am I doing this right?

  1. Sep 27, 2010 #1
    Hi all,

    evaluating [tex]\int\int\int \nabla . V d\tau[/tex] over

    [tex]x^{2} + y^{2} \leq 6, 0 \leq z \leq 10 [/tex]

    where V is a vector function of just [tex]\hat{x} [/tex] and [tex] \hat{y}[/tex].

    Using the divergence theorem, and doing the dot product of V with the normal of the first surface,

    the two partials w.r.t x and y are 2x and 2y,
    doing the cross product, the normal is 4xy z.

    So, the dot product is zero since there is no z component to V?

    Then, when I go to do the same for the second surface, I'm not sure what my double integral limits are, since I only have a surface of z.....

    help!
    thanks!
     
  2. jcsd
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