Use Stokes' Theorem to evaluate the surface integral
∬ G curl F ⋅ n d S
where F ( x , y , z ) = ( z 2 − y ) i + ( x + y z ) j + x z k , G is the surface
G = { ( x , y , z ) | z = 1 − x 2 − y 2 , z ≥ 0 }
and n is the upward point unit normal vector to the surface.
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