**Using the Divergence Theorem to Compute Net Outward Flux**This exercise requires the application of the Divergence Theorem to calculate the net outward flux of the vector field \(\mathbf{F} = (x^2, y^2, z^2)\) over the surface \(S\). Here, the surface \(S\) refers to the sphere defined by the equation \(x^2 + y^2 + z^2 = 4\).**Objective:** Calculate the net outward flux across the surface.**Instructions:**- Type an exact answer, including the use of \(\pi\) as needed.**Hint:** To solve, compute the divergence of the vector field \(\mathbf{F}\) and apply it within the volume integral as specified by the Divergence Theorem.

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Answered: Use the Divergence Theorem to compute…

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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Use the Divergence Theorem to compute the net outward flux of the field F = (x²y²,z²) across the surface S, where S is the sphere {(x,y,z): x² + y² + z² = 4}. The net outward flux across the surface is (Type an exact answer, using as needed.) C