For your surface 2z = x^2 + y^2, this should like a cone:
Cone -- from Wolfram MathWorld
Hey I am working on a problem involving Stokes Theorem, and have found the curl to be <-3y, xz, 0>
So to find the integrand I need to take the dot product of this and the normal vector of the surface, but I am having trouble parametrizing the surface.
The surface is defined as 2z = x^2 + y^2 below the plane z = 1 - y
I need to find the normal vector in terms of two variables and also the bounds of these two variables