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A seemingly simple exercise on the divergence theorem

  1. Jan 8, 2014 #1
    Here is the problem statement:

    I thought it's a straightforward exercise on the divergence theorem, yet it looks like [itex]\operatorname{div} f = 0 [/itex]. So the surface integral is zero?

    Am I missing some sort of a trick here? The exercise isn't supposed to be that easy.

    Any hints are very appreciated!
     
    Last edited: Jan 8, 2014
  2. jcsd
  3. Jan 8, 2014 #2

    BruceW

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    true, ##\operatorname{div} f = 0## but what is the surface? Is it a closed surface or not closed and do they give some specific surface to integrate over?
     
  4. Jan 8, 2014 #3

    LCKurtz

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    If ##S^2## means the unit sphere, then you are correct. Unless there is something missing in the translation of ##(y^3,z^3,x^3)^T##.
     
  5. Jan 8, 2014 #4

    BruceW

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    ah, right, ##S^2## means sphere. I forgot about that. hmm, yeah it looks like zero is the right answer then. well, don't look a gift horse in the mouth :)
     
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