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## Use Stokes’ Theorem to evaluate S curl F · dS. F(x, y, z) = x2 sin(z)i + y2j + xyk, S is the part of the paraboloid z = 9 − x2 − y2 that lie

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## Answers ( )

The vector field

has curl

Parameterize by

where

with and .

Take the normal vector to to be

Then by Stokes’ theorem we have

which has a value of

0, since each component integral is 0: