I'm trying to find the flux of $$\mathbf{F} = x \, \mathbf{i} + (x^2+2z) \, \mathbf{k}$$ out of the space limited by the paraboloid $2z = 1 -x^2 -y^2$ and the $xy$-plane.
I've tried to parametrize from $r(x,y,z)$ to $r(x,y)$ and $r(x,z)$ but they yield impossible integrals to calculate. And at that point spherical/cylindrical coordinates doesn't help either.
Does any one have a good tip?
Cheers,