##curl([x^2z, 3x , -y^3],[x,y,z]) =[-3y^2 ,x^2,3]##
The unit normal vector to the surface ##z(x,y)=x^2+y^2## is ##n= \frac{-2xi -2yj +k}{\sqrt{1+4x^2 +4y^2}}##
##[-3y^2,x^2,3]\cdot n= \frac{-6x^2y +6xy^2}{\sqrt{1+4x^2 + 4y^2}}##
Since ##\Sigma## can be parametrized as ##r(x,y) = xi + yj +(x^2...