# More ASAp help, test in 1 day. divergence theorem

• May 10th 2009, 10:32 AM
ottmar0
More ASAp help, test in 1 day. divergence theorem
use the Divergence Theorem to calculate F Nd omega, where S is the boundary of the cylinder x^2+y^2<orequal to, 0<orequaltoZ<orequal to 3, with outward orientation and F(x,y,z)=<xy^2,yz^2,zx^2>.
• May 10th 2009, 10:49 AM
TheEmptySet
Quote:

Originally Posted by ottmar0
use the Divergence Theorem to calculate F Nd omega, where S is the boundary of the cylinder x^2+y^2<orequal to, 0<orequaltoZ<orequal to 3, with outward orientation and F(x,y,z)=<xy^2,yz^2,zx^2>.

The divergence theorem states that

$\iint_{\partial V}\vec F \cdot d\vec S = \iiint_V \nabla \vec F dV$

$\iiint_V (y^2+z^2+x^2)dV$

Now if we change to cylindrical coordinates we get

$\int_{0}^{3} \int_{0}^{2\pi} \int_{0}^{1}(r^2+z^2)rdr d\theta dz$

Since you didn't give the raduis of the cylindar I assumed it was 1.