Question

How do you go about verifying the divergence theorem for a sphere when given a vector function f(x) and the radius r in Cartesian form?

Answer 1

See here for a unit sphere: http://en.wikipedia.org/wiki/Divergence_theorem#Example Should be able to generalize to sphere of radius r.

Answer 2

so the volume integral of the divergence = flux

Answer 3

(div f). dV = f.dS

Answer 4

is the function a radial function?

Answer 5

\[\int\limits_{?}^{?}\int\limits_{?}^{?} A. ds \]

Answer 6

is it a radial function?

Answer 7

\[A= x^{5} + y ^{5}+z ^{5} \]

Vector

Answer 8

uh oh

Answer 9

how is this a vector fn?

Answer 10

I cnt type a vector with the i, j and k so insert i for x j for y and k for z