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Advanced MathQ&A LibraryUse the Divergence Theorem to evaluate F · dS, where F(x, y, z) = z2xi + + ((1/3)y3 + cos z)j + (x2z + y2)k and S is the top half of the sphere x2 + y2 + z2 = 4. (Hint: Note that S is not a closed surface. First compute integrals over S1 and S2, where S1 is the disk x2 + y2 ≤ 4, oriented downward, and S2 = S1 ∪ S.)Start your trial now! First week only $4.99!*arrow_forward*

Question

Use the Divergence Theorem to evaluate

where

and *S* is the top half of the sphere

x^{2} + y^{2} + z^{2} = 4.

(*Hint*: Note that *S* is not a closed surface. First compute integrals over *S*_{1} and *S*_{2}, where *S*_{1} is the disk

x^{2} + y^{2} ≤ 4,

oriented downward, and *S*_{2} = *S*_{1} ∪ *S*.)

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