Find the flux of the vector field $\displaystyle F(x,y,z) = xi+yj+zk$ through the surface which is part of the paraboloid $\displaystyle S1 = {(x,y,z) \in IR^3; z=x^2+y^2}$ located below the plane $\displaystyle S2 = {(x,y,z) \in IR^3; z=1}$, whereas the vector normal to the surface points to the external side of the paraboloid

my parameterization:
$\displaystyle r(t) = (vcosu,vsinu,v))$

$\displaystyle \frac{\partial r}{\partial u} x \frac{\partial r}{\partial v} = (vcosu, vsinu, -vsin^2u-vcos^2u)$

Now what do I need?