Problem. 9 : Use the Divergence Theorem to calculate the surface integral ff F - :13, where S 3 F(r,y,z) = $z2i+ (y? + cos{z]) j+ (322+ yg) k and S is the top half of the sphere $2 + y?' + 2 2 9. Note that S is not a closed surface. Filst, compute the integrals over S1 and 3'2, Where S1 is the disk 32 + 3,12 '3 9, oriented downward, and 32 = S] U S is a closed surface. ffF-dh ff aw S; shy-'39 52 is closed and by the Divergence Theorem we have Finally