12. Given the vector field F(x, y, z) = (x² - z²)i + (x + 3z)j + (x² - z)k and S is the surface of the solid bounded by the cylinder x² + y² = 36 and the planes z = -2 and z = 3. Use the Divergence Theorem to evaluate the outward flux of F through the surface S. Show work.
12. Given the vector field F(x, y, z) = (x² - z²)i + (x + 3z)j + (x² - z)k and S is the surface of the solid bounded by the cylinder x² + y² = 36 and the planes z = -2 and z = 3. Use the Divergence Theorem to evaluate the outward flux of F through the surface S. Show work.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:12. Given the vector field F(x, y, z) = (x² - z²)i + (x + 3z)j + (x² - z)k and S is the surface of
the solid bounded by the cylinder x² + y² = 36 and the planes z = -2 and z = 3.
Use the Divergence Theorem to evaluate the outward flux of F through the surface S.
Show work.
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