Find the flux of F across S. For closed surfaces, use the positive orientation.
F(x,y,z) = xy i +yz j + zx k
S is the part of the paraboloid z = 4 - x^2 - y^2 that lies above the square 0 <= x <= 1 and 0 <= y <= 1 and has upward orientation.
The part that's confusing me is finding an appropriate paramaterization.