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#2
Sep13-06, 01:43 PM
HW Helper
P: 2,567
Gauss's theorem states:

[tex]\int_A (\nabla \cdot \vec F) dV = \int_{\partial A} \vec F \cdot d \vec A[/tex]

Where [itex]A[/itex] is a volume in space and [itex]\partial A[/itex] is its bounding surface. If you can find a vector function [itex] \vec F[/itex] with [itex]\nabla \cdot \vec F=1[/itex], then the LHS, and so also the RHS, is equal to the volume of A.