Evaluate $\int\int_SF.dS$ where $F=(xz,yz,x^2+y^2)$
Where $S$ is the closed surface obtained from the surfaces $x^2+y^2\leq 4,z=2,x^2+y^2\leq 16,z=0$ on the top and the bottom and $z=4-\sqrt{x^2+y^2}$ on the side.
How we can solve such integrals?I need your help.
Edit: without using the Gauss Divergence theorem.