Use the Divergence Theorem to evaluate S F dS, where F(x, y, z) = z

Use the Divergence Theorem to evaluate ʃʃ_S F π dS, where F(x, y, z) = z²x i + (1/3y³ + tan z) j + (x²z + y² ) k and S is the top half of the sphere x² + y² + z² = 1.

That S is not a closed surface. First compute integrals over S₁ and S₂, where S₁ is the disk x² + y² < 1, oriented downward, and S₂ = S U S₁.]