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

Question:

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

F(x, y, z)= e^xy cos zi + x²zj + xyk, S is the hemisphere x = √1 – y² – z², oriented in the direction of the positive x-axis

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