In: Math
Use the Divergence Theorem to evaluate
S |
F · dS,
where
F(x, y, z) = z2xi +
y3 |
3 |
+ cos z
j + (x2z + y2)k
and S is the top half of the sphere
x2 + y2 + z2 = 4.
(Hint: Note that S is not a closed surface. First compute integrals over S1 and S2, where S1 is the disk
x2 + y2 ≤ 4,
oriented downward, and S2 = S1 ∪ S.)