Evaluate the surface integral S F dS for the given vector field F and the oriented surface S. In other words, find the

Evaluate the surface integral ʃʃ_S F • dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x, y, z) = y i - x j + 2z k, S is the hemisphere x² + y² + z² = 4, z > 0, oriented downward