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Divergence theorem problem

  1. Dec 6, 2014 #1

    s3a

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    1. The problem statement, all variables and given/known data
    Find the outward flux of the radial vector field F(x,y,z) = x i^ + y j^ + z k^ through the boundary of domain in R^3 given by two inequalities x^2 + y^2 + z^2 ≤ 2 and z ≥ x^2 + y^2.

    2. Relevant equations
    Divergence theorem: ∫∫_S Fn^ = ∫∫∫_D div F dV

    3. The attempt at a solution
    Is the final answer correct in TheSolution.jpg (because I get 2*pi/3 * (2^(3/2) - 1) - pi/2)?

    If someone could check if I'm right or wrong, I would REALLY appreciate it!
     

    Attached Files:

  2. jcsd
  3. Dec 6, 2014 #2

    s3a

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    Actually, I get π * [2(2^[3/2] - 1) - 3/2] (where my answer's 2^[3/2] differs with the √(2) in the attachment).
     
    Last edited: Dec 6, 2014
  4. Dec 6, 2014 #3

    Zondrina

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    Homework Helper

    There appears to be a typo near the front of the answer. That ##2## should not be in front of the divergence integral.
     
  5. Dec 6, 2014 #4

    s3a

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    Thanks for pointing that out.

    Are the parts where the author begins to use the letter "t" and, most importantly, the final answer correct?
     
  6. Dec 7, 2014 #5

    Zondrina

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  7. Dec 7, 2014 #6

    s3a

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    Actually, my answer (from the second post in this thread) is the same as three times yours, so it appears that I was correct and that the solution was incorrect.

    I'm posting my latest work, just in case I'm right by fluke (so please confirm).
     

    Attached Files:

  8. Dec 7, 2014 #7

    Zondrina

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    Sorry about that. I forgot the 3 so the answer should be 6.78.
     
  9. Dec 7, 2014 #8

    s3a

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    That's the same thing I got (and not what the solution that I attached in my first post in this thread got).

    It must not have seemed like a lot to you, but your confirmation was very helpful to me, so thanks for helping me confirm! :)
     
  10. Dec 7, 2014 #9

    Zondrina

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    Homework Helper

    Wolfram is good for self error checking, but matlab's dblquad and triplequad functions are also a very good option.
     
  11. Dec 7, 2014 #10

    s3a

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    Thanks as well for mentioning those, but I meant having another human being to confirm was useful, because I'm stressed and exhausted and studying for exams, so I wanted to make sure I wasn't making a mistake in the setup of the computation (because one makes more mistakes when stressed and/or exhausted).
     
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