Solution: Evaluate this integral by the divergence theorem.

Chapter 10, Problem 10.1.156

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

\(\mathbf{F}=\left[x^{3}-y^{3}, y^{3}-z^{3}, z^{3}-x^{3}\right], S\) the surface of \(x^{2}+y^{2}+z^{2} \leqq 25, z \geqq 0\)

Text Transcription:

F = [x^3 - y^3, y^3 - z^3, z^3 - x^3], S

x^2 + y^2 + z^2 leqq 25, z geqq 0

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