Hi there. I was trying to solve this problem, from the book. The problem statement says:

Integrate over the portion of the surface under the plane z=2, directly and using Stokes theorem.

So I started solving the integral directly. For the rotational I got:

Then I parametrized the surface.:

Then I did:

For the cross product I got:

And then I computed the integral

The result given by the book is: .

I don't know what I did wrong, and is one of the first exercises that I've solved for the stokes theorem, so maybe I could get some advices and corrections from you

Thank you in advance. Bye.