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

Use the Divergence Theorem to evaluate

F · dS,

where

F(x, y, z) = z²xi +

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.)

Solutions

Expert Solution

milcah answered 1 year ago

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