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

F(x, y, z) = x²z² i + y²z²j + xyz k, S is the part of the paraboloid z = x² + y² that lies inside the cylinder x² + y² = 4, 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