Evaluate the surface integral:
where S is part of the surface of the paraboloid in the second octant.
First of all, I hope the second octant is where x is negative but y and z are positive? (well, or 0).
Let then and which is normal to the surface S.
Then in polar coords, in the 2nd octant, we have:
since the shadow D on the xy-plane is a unit circle and,
in the 2nd oct.
So the integral is:
. Right so far?
Now the problem is, I don't see any simple way to integrate this... I don't think u-substitution will help me here, but could be wrong.