Consider the solid G bounded above by z =sqrt(4 − x^2 − y^2) and below by z =√3. Let σ be the surface of G oriented by outward normals. Let F(x, y, z) = ⟨x, y, 2⟩ be a vector field. (a) Sketch σ accurately. (b) Find the flux of F over σ exactly. Simplify your answer. No decimal approximations.

Consider the solid G bounded above by z =sqrt(4 − x^2 − y^2) and below by z =√3. Let σ be the surface of G oriented by outward normals. Let F(x, y, z) = ⟨x, y, 2⟩ be a vector field. (a) Sketch σ accurately. (b) Find the flux of F over σ exactly. Simplify your answer. No decimal approximations.

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

Consider the solid G bounded above by z =sqrt(4 − x^2 − y^2) and below by z =√3.
Let σ be the surface of G oriented by outward normals. Let F(x, y, z) = ⟨x, y, 2⟩ be a vector field.
(a) Sketch σ accurately.
(b) Find the flux of F over σ exactly. Simplify your answer. No decimal
approximations.

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