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Set up the triple integral that will give the following: (a) the volume of R using cylindrical coordinates with dV= r dz dr de where R: 0≤ x ≤ 1,0 ≤ y ≤ √1-x², 0≤x≤ √√4-(x² + y²). Draw the solid R.

Set up the triple integral that will give the following: (a) the volume of R using cylindrical coordinates with dV= r dz dr de where R: 0≤ x ≤ 1,0 ≤ y ≤ √1-x², 0≤x≤ √√4-(x² + y²). Draw the solid R.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 40E: For the sphers x-12+y+22+z-42=36 and x2+y2+z2=64, find the ratio of their a surface areas. b...
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6. Set up the triple integral that will give the following: (a) the volume of R using cylindrical coordinates with dV = r dz dr de where R: 0< x ≤ 1,0 ≤ y ≤√1-x², 0≤ z ≤ √√4-(x² + y²). Draw the solid R. (b) the volume of the solid B that lies above the cone z = 3r²+3y² and below the sphere 2² + y² + z² = z using spherical coordinates. Draw the solid B 8
Transcribed Image Text:6. Set up the triple integral that will give the following: (a) the volume of R using cylindrical coordinates with dV = r dz dr de where R: 0< x ≤ 1,0 ≤ y ≤√1-x², 0≤ z ≤ √√4-(x² + y²). Draw the solid R. (b) the volume of the solid B that lies above the cone z = 3r²+3y² and below the sphere 2² + y² + z² = z using spherical coordinates. Draw the solid B 8
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