Verify that Stokes Theorem is true for the given vector field F and surface S.

F(x, y, z) = xi + yj + xyz k, S is the part of the plane 2x + y + z = 2 that lies in the first octant, 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