Surface integral of a paraboloid of revolution

Question

Assignment:

Let S be the closed surface of the paraboloid of revolution z = ±(4 − x²  − y² ) where −2≤x, y≤+2. Evaluate the following surface integral directly and then by using the divergence theorem;

I =  ∫_s R.n^{^}dA

where R is the position vector to a point on the surface and  n^{^} is the outward pointing normal at that point.

Provide complete and step by step solution for the question and show calculations and use formulas.