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Volume of a closed surface (divergence theorem)

  1. Dec 28, 2013 #1
  2. jcsd
  3. Dec 28, 2013 #2

    SteamKing

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    Green's and Stokes' theorems can by used on surface integrals, just like they are used for 2-D integrals.

    The math is a little more complex, however.

    Google: 'line surface and volume integrals'
     
  4. Dec 28, 2013 #3
  5. Dec 28, 2013 #4
  6. Dec 28, 2013 #5
    I am searching for something similar to this:
    f76df7ea16919c17fe62cef9eb303fd7.png


    EDIT: I think that the volume can be calculated by:
    [tex]V=\iint_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset xdydz = \iint_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset ydzdx = \iint_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset zdxdy = \frac{1}{3}\iint_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset (xdydz+ydzdx+zdxdy)[/tex]

    Correct?
     
    Last edited: Dec 29, 2013
  7. Dec 30, 2013 #6
    This equation is really correct?
     
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