Answered: (a) Obtain the equations of the… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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Question

3. Calculate the following triple integral:
I
¹ = [[ ] ₁ ₁
S
where the solid S is defined as follows:
1
x² + y² + 2²
dxdydz
S = {(x, y, z) € R³ : z² ≤ x² + y² ≤ 2z − 2²}
(a) Obtain the equations of the surfaces involved and sketch/describe the solid S.
(b) Perform the integration in cylindrical coordinates.
(c) State whether, in your opinion, it is better to proceed with an integration via
cross-section method or shadow method. Both methods could also be equally
applicable and there could be no "better" choice. Elaborate on your reasoning in
any case.
(d) Write down the integral limits for both cases (cross-section method and shadow
method), without performing the integration.

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