Question

Find flux of F=(3xyy, 3xxy, 3zzz) out of sphere R=2. Flux is given by 2^5S(a->b)S(c->d) f(theta,phi) d(theta)d(phi). What is f? No Div Thm.

Answer 1

Find the flux of F given above out of the sphere of radius 2. "Hint: use spherical coordinates and be mindful of orientation." The flux is given by 2\[^{5}\]\[\int\limits_{a}^{b}\]\[\int\limits_{c}^{d}\] f(\[\Theta\],\[\Phi\]) d\[\Theta\]d\[\Phi\]

Find f. (Solve directly; do not use alternative methods to solve such as Divergence Theorem)

Answer 2

You have to parametrize the sphere, see example 2 here.

Answer 3

oops forgot link, http://tutorial.math.lamar.edu/Classes/CalcIII/SurfaceIntegrals.aspx