**Problem Statement**Use the extended divergence theorem to compute the total flux of the vector field \[\vec{F}(x, y, z) = (-5x^2 + 3xz - y, \, 4y^3 - 6y, \, 9x^2 + 4z^2 - 3x)\]outward from the region $ F $ that lies inside the sphere $ x^2 + y^2 + z^2 = 25 $ and outside the solid cylinder $ x^2 + y^2 = 4 $ with top at $ z = 1 $ and bottom at $ z = -1 $.

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Use the extended divergence theorem to compute the total flux of the vector field F(x, y, 2) 3D (-5х2 + 3xz - у, 4у3 - бу, 9х2 + 422 - 3х) outward from the region F that lies inside the sphere x2 + y? + z2 = 25 and outside the solid cylinder x + y? = 4 with top at z = 1 and bottom at z = -1.

Use the extended divergence theorem to compute the total flux of the vector field F(x, y, 2) 3D (-5х2 + 3xz - у, 4у3 - бу, 9х2 + 422 - 3х) outward from the region F that lies inside the sphere x2 + y? + z2 = 25 and outside the solid cylinder x + y? = 4 with top at z = 1 and bottom at z = -1.

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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Question

**Problem Statement**

Use the extended divergence theorem to compute the total flux of the vector field

\[
\vec{F}(x, y, z) = (-5x^2 + 3xz - y, \, 4y^3 - 6y, \, 9x^2 + 4z^2 - 3x)
\]

outward from the region $ F $ that lies inside the sphere $ x^2 + y^2 + z^2 = 25 $ and outside the solid cylinder $ x^2 + y^2 = 4 $ with top at $ z = 1 $ and bottom at $ z = -1 $.

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