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following solids. Do not evaluate your integral. (a) The solid lying inside the sphere ²+²+²=9, inside the cylinder a² + y² = 4, and above the plane z=0. (b) The solid enclosed by the cylinder 2² + y² = 1 and the planes y += 1 and 2y+z=2. (e) The solid lying between the paraboloids=²+2y² and 23-22²-² (d) The solid lying between the spheres ²+²+²-1 and 22+²+²=4 and above the cone √²+².

following solids. Do not evaluate your integral. (a) The solid lying inside the sphere ²+²+²=9, inside the cylinder a² + y² = 4, and above the plane z=0. (b) The solid enclosed by the cylinder 2² + y² = 1 and the planes y += 1 and 2y+z=2. (e) The solid lying between the paraboloids=²+2y² and 23-22²-² (d) The solid lying between the spheres ²+²+²-1 and 22+²+²=4 and above the cone √²+².

Advanced Engineering Mathematics
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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1. Use cylindrical or spherical polar coordinates to set up an integral for the volume of the following solids. Do not evaluate your integral. (a) The solid lying inside the sphere ²+²+²=9, inside the cylinder ² + y² = 4, and above the plane z=0. (b) The solid enclosed by the cylinder 27+y=1 and the planes y += 1 and 2y += = 2. (e) The solid lying between the paraboloids :=²+2y² and 3-22²-² 2 (d) The solid lying between the spheres ²+²+²-1 and 2²+²+²=4 and above the cone = √2+y.
Transcribed Image Text:1. Use cylindrical or spherical polar coordinates to set up an integral for the volume of the following solids. Do not evaluate your integral. (a) The solid lying inside the sphere ²+²+²=9, inside the cylinder ² + y² = 4, and above the plane z=0. (b) The solid enclosed by the cylinder 27+y=1 and the planes y += 1 and 2y += = 2. (e) The solid lying between the paraboloids :=²+2y² and 3-22²-² 2 (d) The solid lying between the spheres ²+²+²-1 and 2²+²+²=4 and above the cone = √2+y.
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