Consider the solid E determined by the inequalitiesx² + y² + z ≤ 4,and let S denote the surface bounding E.(a) Find the surface area of S.(b) What is the outward flux of the vector field F = (y, z², 5z + ln(x² + y²)) across S?(c) What about the outward flux of curl(F) across the part of S where x² + y² + z = 4?x² + y² ≥ 1,z ≥ 0,

Answered: Consider the solid E determined by the…

Consider the solid E determined by the inequalities x² + y² + z≤ 4, and let S denote the surface bounding E. (a) Find the surface area of S. x² + y² ≥ 1, z ≥ 0,

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 E determined by the inequalities
x² + y² + z ≤ 4,
and let S denote the surface bounding E.
(a) Find the surface area of S.
(b) What is the outward flux of the vector field F = (y, z², 5z + ln(x² + y²)) across S?
(c) What about the outward flux of curl(F) across the part of S where x² + y² + z = 4?
x² + y² ≥ 1,
z ≥ 0,

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