# Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 +

###### Question:

Use the Divergence Theorem to evaluate S

F · dS,

where

F(x, y, z) = z2xi + y3 3

+ sin 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 = S1S.) 6. 0/10 points | Previous Answers SCalc8 16.9.017 My Notes Ask Your -z2ri + r2z + y2 k and s is the top half of the sphere r 2 . r Use the Divergence Theorem to evaluate F where F х, у z sed surt ce First compute d + . 4. int Note that Sis not a + s n z integrals over S1 and S2, where S1 is the disk x2 +y2s 4, oriented downward, and S2 -S1 U S.) 486 1-4 Talk to a Tuter Submit Answer Save Progress Practice Another Version ec View Previous Question Question 6 of 10 View Next Question >> Home My Assignments Extension Request

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