# Divergence Theorm example for 28 Nov 12:00

by debian
Tags: 1200, divergence, theorm
 P: 7 1. The problem statement, all variables and given/known data Let S be a smooth surface enclosing the volume V, and let $\vec{n}$ to be the unit outward normal. Using the Divergence Theorm show that: ∫∫ x $\vec{r}$ ° $\vec{n}$ dS = 4 * ∫∫∫ x dV, where $\vec{r}$=(x,y,z) 2. Relevant equations Divergence theorm http://www.math.oregonstate.edu/home...rg/diverg.html 3. The attempt at a solution I tried to change the form of the those two equations to the form stated in divergence theorm and then to compare the u (or F as in link above), but the u (F) on the left hand side is never equal to this on the right.
 P: 939 Your link is broken. But let's suppose the divergence theorem says $$\iint (\vec{F} \cdot \vec{n}) dS = \iiint \nabla \cdot \vec{F} dV.$$ Now you are given $\vec{F}= x \vec{r}$. Can you calculate $\nabla \cdot \vec{F}$?
 P: 7 $\nabla$ $\cdot$ $\vec{F}$ = (d/dx, d/dy, d/dz) $\cdot$ (x^2,xy,xz) = 2x+x+x=4x
 Quote by debian $\nabla$ $\cdot$ $\vec{F}$ = (d/dx, d/dy, d/dz) $\cdot$ (x^2,xy,xz) = 2x+x+x=4x