Evaluate the surface integral:

where S is part of the surface of the paraboloid

in the second octant.

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First of all, I hope the second octant is where x is negative but y and z are positive? (well, or 0).

Second,

Let

then

and

which is normal to the surface S.

EDIT: so

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.