Volume of a closed surface (divergence theorem)

[Jhenrique]

If exist a formula for calculate the area of a closed curve: http://en.wikipedia.org/wiki/Green's_theorem#Area_Calculation, so, there is a analogous for calculate the volume of a closed surface? I search but I not found...

 

[SteamKing]

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'

 

[Jhenrique]

I found nothing similar to this: http://en.wikipedia.org/wiki/Green's_theorem#Area_Calculation

 

[Number Nine]

I found nothing similar to this: http://en.wikipedia.org/wiki/Green's_theorem#Area_Calculation

First search result:
http://www.physics.nus.edu.sg/~phylimhs/LineSurfVolInt2.pdf

Page 30 relates the volume of a region to an integral over its boundary.

 

[Jhenrique]

I am searching for something similar to this:

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

Correct?

 

[Jhenrique]

$$V=\iint_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset xdydz = \iint_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset ydzdx = \iint_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset zdxdy = \frac{1}{3}\iint_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset (xdydz+ydzdx+zdxdy)$$

This equation is really correct?