Use Stokes Theorem to evaluate ∫_C F · dr. In each case C is oriented counterclockwise as viewed from above.

F(x, y, z) = xyi + 2zj + 3yk, C is the curve of intersection of the plane x + z = 5 and the cylinder x² + y² = 9

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