1. Compute the surface integral  where F(x,y,z) = yi - xj - 3k and S is the surface of the paraboloid z = x² + y² (with upward orientation) within the cylinder x² + y² = 1.
 
 
 
 
 
 

2. Use Stokes' Theorem to compute  where S is the top half of a sphere of radius 3 centered at the origin with upward orientation and F(x,y,z) = xi + yj + zk [Note that it should come out to zero, since curl F = 0, but show that Stokes' gives zero too].