Let E be the solid that lies above the cone z = 3r2 + 3y? and below the sphere r²+y² + z² = 4. (a) Sketch the solid E. (b) Using symmetry, set up a triple integral in rectangular coordinates representing the volume of E. Do not evaluate the integral. (c) Again using symmetry, set up a triple integral in cylindrical coordinates representing the volume of E. Do not evaluate the integral. (d) Set up a triple integral in spherical coordinates representing the volume of E. Do not evaluate the integral.
Let E be the solid that lies above the cone z = 3r2 + 3y? and below the sphere r²+y² + z² = 4. (a) Sketch the solid E. (b) Using symmetry, set up a triple integral in rectangular coordinates representing the volume of E. Do not evaluate the integral. (c) Again using symmetry, set up a triple integral in cylindrical coordinates representing the volume of E. Do not evaluate the integral. (d) Set up a triple integral in spherical coordinates representing the volume of E. Do not evaluate the integral.
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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Transcribed Image Text:/3r² + 3y² and below the sphere r? +y? + 2² = 4.
Let E be the solid that lies above the cone z
(a) Sketch the solid E.
(b) Using symmetry, set up a triple integral in rectangular coordinates representing the volume
of E. Do not evaluate the integral.
(c) Again using symmetry, set up a triple integral in cylindrical coordinates representing the
volume of E. Do not evaluate the integral.
(d) Set up a triple integral in spherical coordinates representing the volume of E. Do not
evaluate the integral.
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