Use Stokes' Theorem to compute the integral ∫∫_S curl F · dS, where F(x, y, z) = xz i + yz j+ xy k and S is the part of the sphere x² + y² + z² =  4 that lies inside the cylinder x² + y² = 1 and above the xy-plane. (See Figure 4.)

Figure 4

Stokes' Theorem

xx N 0 S C x + y + z = 4 y x + y = 1