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Use Stokes' Theorem to evaluate the surface integral ∬ G curl F ⋅ n d S...

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.

Math   Calculus   
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