Volume of a closed surface (divergence theorem)

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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'
 
685
4
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:
685
4
[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]
This equation is really correct?
 

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