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Evaluate by converting to cylindrical coördinates. 3. The volume of the solid enclosed by z = 36 - 3x² − 3y² and z= x² + y²

Evaluate by converting to cylindrical coördinates. 3. The volume of the solid enclosed by z = 36 - 3x² − 3y² and z= x² + y²

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 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
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JJR * Evaluate by converting to polar coördinates. J₂ (√4-x² - y²) 2. + * Evaluate by converting to cylindrical coördinates. 3. The volume of the solid enclosed by z = 36-3x² − 3y² and z= x² + y² dA R given by x² + y² ≤4 with x ≥ 0 * Evaluate by converting to spherical coördinates. 4. The volume of the solid in the first octant bounded by x² + y² + z² = 4,0 = ¹/6 5. Evaluate x = t² [(z)dx + (z)dx + (x)dy + (y)dz C given by y = t³ for 0 ≤t≤1 z = t²
Transcribed Image Text:JJR * Evaluate by converting to polar coördinates. J₂ (√4-x² - y²) 2. + * Evaluate by converting to cylindrical coördinates. 3. The volume of the solid enclosed by z = 36-3x² − 3y² and z= x² + y² dA R given by x² + y² ≤4 with x ≥ 0 * Evaluate by converting to spherical coördinates. 4. The volume of the solid in the first octant bounded by x² + y² + z² = 4,0 = ¹/6 5. Evaluate x = t² [(z)dx + (z)dx + (x)dy + (y)dz C given by y = t³ for 0 ≤t≤1 z = t²
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