Question

In: Math

Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi...

Use the Divergence Theorem to evaluate

S

F · dS,

where

F(x, y, z) = z2xi +

y3
3

+ 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 = S1S.)

Solutions

Expert Solution


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