# Volume of a closed surface (divergence theorem)

#### Jhenrique

Related Differential Geometry News on Phys.org

#### SteamKing

Staff Emeritus
Homework Helper
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 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?

Last edited:

#### 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?

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