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Homework Help: A volume integral over a sphere

  1. Mar 16, 2013 #1
    1. The problem statement, all variables and given/known data

    ∫∫∫∇.Fdv over x2+y2+z2≤25

    F= (x2+y2+z2)(xi+yj+zk)

    2. Relevant equations

    ∫∫∫∇.Fdv = ∫∫ F.n dσ


    3. The attempt at a solution


    taking the surface integral and replacing all
    (x2+y2+z2) with 25
    i got
    125 * ∫∫ dσ = 12500π

    But the answer key says it is 100π
    I think i am making a mistake with numbers but, i couldn't find what is wrong.

  2. jcsd
  3. Mar 16, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I don't think anything is wrong except the answer key.
  4. Mar 17, 2013 #3
    Hmm, ok then, thanks.
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