Use Stokes Theorem to evaluate S curl F ds.k F(x, y, z) = 2y cos

Question:

Use Stokes Theorem to evaluate ∫∫_S curl F · ds.k

F(x, y, z) = 2y cos zi + e^xsin zj + xe^y k, S is the hemisphere x² + y² + z² = 9, z ≥ 0, oriented upward

Data from Stokes Theorem

Let S be an oriented piecewise-smooth surface that is bounded by a simple, closed, piecewise-smooth boundary curve C with positive orientation. Let F be a vector field whose components have continuous partial derivatives on an open region in R³ that contains S. Then

S F dr = ff S curl F. ds