Evaluating Surface Integral with Stokes Theorem

[trelek2]

use the stokes theorem to evaluate the surface integral [curl F dot dS] where
F=(x^2+y^2; x; 2xyz)
and S is an open surface x^2+y^2+z^2=a^2 for z>=0. So i guess its a hemisphere of radius a lying on x-y plane.
I don't see however how to take F dot dr. What is this closed curve dr bounding this hemisphere? I guess we can take spherical polar coordinates, but still once i have x,y,z in terms of r,phi,theta i still don't know "dr" (just differentiate ?) and what will the limits of integration be? Can someone show me?

 

[dx]

The boundary of the surface is just the circle x² + y² = a² in the xy plane. Did you try drawing a picture?