1. The problem statement, all variables and given/known data Let S be the part of the paraboloid [itex]z=1+x^2+y^2[/itex] lying above the rectangle x between 0 and 1; y between -1 and 0 and oriented by the upward normal. Compute [itex]\int\int_SF\cdot n\,dS[/itex] where F=<xz, xy, yz> So I have Parametrized the surface S as r(x,y,z)=<x, y, 1+x2+y2> Then I have found dr\dx cross dr/dy =f then I found F(r(x,y)) dot f Now I need to integrate this over the domain of E but I am having trouble finding my bounds for x and y? I need to project the paraboloid downward onto x-y plane right? This gives a curve, oh wait, the curve is just the equation of the paraboloid with z=0 right? So the curve is 1+x2+y2=0 why does that not sit well with me?