# Volume of a closed surface (divergence theorem)

1. Dec 28, 2013

### Jhenrique

2. Dec 28, 2013

### SteamKing

Staff Emeritus
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'

3. Dec 28, 2013

### Jhenrique

4. Dec 28, 2013

### Number Nine

5. Dec 28, 2013

### 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: Dec 29, 2013
6. Dec 30, 2013

### Jhenrique

This equation is really correct?