$($a$)$ Set up a double integral for calculating the flux of the vector field vec$(F)(x,y,z)=-2$xzvec$(i)-2$yzvec$(j)+z^2$vec$(k)$ through the part of the cone $z=\sqrt[\phantom{2}]{x^2+y^2}$ for $0z2,$ oriented upward.

Flux $={}_{\text{D}\text{i}\text{s}\text{k}}dxdy$

$($b$)$ Evaluate the integral.

Flux $={}_S$vec$(F)*dvec(A)=24$

Hint:

Note: You can earn partial credit on this problem.