Answer: Evaluate this integral by the divergence theorem.

Chapter 10, Problem 10.1.153

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Evaluate this integral by the divergence theorem. (Show the details.)

\(\mathbf{F}=\left[\begin{array}{lll}z-y & \mathrm{y}^{3}, & 2 z^{3}\end{array}\right], S\) the surface of \(y^{2}+z^{2} \leqq 4\), \(-3 \leqq x \leqq 3\)

Text Transcription:

F = [z - y  y^{3},  2z^3], S

y^2 + z^2 leqq 4

-3 leqq x leqq 3

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