# Divergence over a Region

The Divergence Theorem says that if a region, D, is bound by a closed curve,
then the integral of the divergence over that region is equal to the
**flux** across the boundary. This is often written:
.

But what does this mean? Let `g(t), t=0..T,`

parameterize the
boundary in a counter-clockwise fashion. If *n(t)* is the unit normal to *g(t)*, then we can make sense of the right-hand integral
by writing

## Question #2

In this question we will evaluate the double integral
on the left by computing the line integral on the right.
- Parametrize the unit circle about the stable equilibrium (the sink)
by
`g(t), t=0..2*Pi.`

Note: The sink is **not**
at the origin!
- Compute the tangent vector
*g'(t)* and use this to
write down the **unit** normal vector to the circle.
- Use Maple to help you compute the dot product of
*f(g(t))*
and *n(t)* and the integral of this dot product times the
length of *g'(t)* from `t=0..2*Pi`

.

We've provided a hint
in case you get stuck.
Next: The Average Divergence

Up: Introduction

Previous: Divergence at a Point

Frederick J. Wicklin <fjw@geom.umn.edu>
Brian Burt<burt@geom.umn.edu>
Document Created: Wed Jan 25 CST

Last modified: Tue Mar 14 10:27:25 1995