Use Stokes' Theorem to evaluate

Question

S
curl F · dS.
F(x, y, z) = 2y cos z i + ex sin z j + xey k,

S is the hemisphere x2 + y2 + z2 = 49, z ≥ 0, oriented upward.

Answer 1

The curve for the line integral is just

x = 9cos(t)
y = 9sin(t)
z = 0

Now just evaluate F.dr and integrate for t in [0,2pi]