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. (b) the volume of the solid B that lies above the cone z = /3x² + 3y2 and below the sphere x² + y² + z² = z using spherical coordinates. Draw the solid B

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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 ≤ z ≤ √4 − (x² + y²). Draw the solid R.
(b) the volume of the solid B that lies above the cone z = 3x² + 3y² and below the
sphere x² + y² + z² = z using spherical coordinates. Draw the solid B
Transcribed Image Text: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 = 3x² + 3y² and below the sphere x² + y² + z² = z using spherical coordinates. Draw the solid B
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