Consider the region E = {(x, y, z) : x² + y²+z² < 1, ]x| < y}. (a) Describe the region E in spherical coordinates. [Hint: It might be helpful to think of what the slice of this looks like in the xy-plane.]

Consider the region E = {(x, y, z) : x² + y²+z² < 1, ]x| < y}. (a) Describe the region E in spherical coordinates. [Hint: It might be helpful to think of what the slice of this looks like in the xy-plane.]

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

9.
Consider the region E = {(x, y, z) : x² + y? + z² < 1, |æ| < y}.
(a) Describe the region E in spherical coordinates. [Hint: It might be helpful to think of what the slice of
this looks like in the xy-plane.]
(b) Set up – but do not evaluate – an integral to compute the volume of E.

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