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## Main Question or Discussion Point

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?

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?