Divergence Theorem

The divergence theorem establishes the volume integral (triple integral) of a function over a three-dimensional shape equals the double integral of the same function over the two-dimensional surface that encloses the space.

For example, the volume integral of the electric field caused by a charge within an electric sphere equals the surface integral of that same field.

This is also known as the Gauss Theorem, and it is the simplest of the three main integral theorems in advanced or multivariable calculus, the other two being Green's Theorem and Stokes' Theorem.