Use Stokes' Theorem to evaluate http://www.math.umn.edu/~nykamp/m237...sidea/img6.gif
F(x,y,z)=(x^2)(z^2)i+(y^2)(z^2)j+xyzk, S is the part of the paraboloid z=x^2+y^2 that lies inside the cylinder x^2+y^2=4, oriented upward:confused:

Because it is oriented upward, we can parametrize S:





Now, use those in

Find your curl F by taking the cross product



There's a start.