calculate the flux of F = (z,4,-xy) out of the sphere x^2 + y^2 +z^2 = 4
cheers
Oh blast! I wrote out a whole long treatise on how to find the vector differential of surface area and then realized it is far easire to use the "divergence theorem".
That says that $\displaystyle \oint\oint \vec{F}\cdot d\vec{S}= \int\int\int \nabla\cdot\vec{F} dV$.
And, for $\displaystyle \vec{F}= z\vec{i}+ 4\vec{j}- xy\vec{k}$, $\displaystyle \nabla\cdot\vec{F}= \vec{0}$!