Question

Use Stokes' Theorem to evaluate S ∫ F · dS. F(x, y, z) = x2 sin(z)i + y2j + xyk, S is the part of the paraboloid z = 4 − x2 − y2 that lies above the xy-plane, oriented upward.

Answer 1

Look at the image,

Explanation:

This is an explanation of the same exercise but when the paraboloid is z = 9 − x2 − y2. In that case you just have to replace 9 by 4 and follow the same steps :).