Ex: Find the center of mass of the solid whose density &z and bounded above by the plane z=y, below by the xy-plane and laterally by the cylinder x² + y² = 4. Sol.: M = SSS 8dv π 2 rsine =[[[ 000 2 =]] //² 00 Mxy zrdzdrd0 = r³ sin² 0 drd0 = 10 π 2 rsine 00 0 π 2 00 T π 2 00 1/16 [+][0-sin20] =(1-0) (1 - 0) = π rsine ¹0 zdrdzdrd0 = drdo r³(1-cos20) drde ·SSS 000 π 2 rsine z²rdzdrde zy x²+²=4 x-0 # J=12 -2 2 r=2 r=2
Ex: Find the center of mass of the solid whose density &z and bounded above by the plane z=y, below by the xy-plane and laterally by the cylinder x² + y² = 4. Sol.: M = SSS 8dv π 2 rsine =[[[ 000 2 =]] //² 00 Mxy zrdzdrd0 = r³ sin² 0 drd0 = 10 π 2 rsine 00 0 π 2 00 T π 2 00 1/16 [+][0-sin20] =(1-0) (1 - 0) = π rsine ¹0 zdrdzdrd0 = drdo r³(1-cos20) drde ·SSS 000 π 2 rsine z²rdzdrde zy x²+²=4 x-0 # J=12 -2 2 r=2 r=2
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
Section10.1: The Rectangular Coordinate System
Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...
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