Divergence Theorem

Let $E$ be a Simple Solid.

Let the surface $S$ be the boundary surface enclosing $E$, with outward orientation.

Let the vector field $\vec{F}$ have continous partial derivatives on the open region that contains $E$

$${\iint }_S\vec{F}\cdot d\vec{S}={\iiint }_E\nabla \cdot \vec{F}dV$$

• Vector Surface Integral equal Triple Integral of the Divergence
• “Blow a bubble around $E$ in the shape of $S$, and it will tell you how much the inside of the bubble wants to run away”