I'm having difficulty to find the surface integral using Stoke's Theorem, can anyone please help? Help will be much appreciated!
I'm learning exactly the same subject so I might be wrong.
I believe the following : the surface of the sphere is $\displaystyle x^2+y^2+z^2=4$ with the restriction of the first octant.
So $\displaystyle z=\sqrt {4-x^2-y^2}$. You're integration over the circle $\displaystyle x^2+y^2=4$ so the boundaries of the surface integral would be $\displaystyle \int _0^{\frac{\pi}{4}} \int _0^{2} F dA$. Notice that I used polar coordinates.
I'm not sure though, so I'll wait any further help.