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1) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. ?=1−?^4,?=0; about ?=2  2)  Use cylindrical shells to find the volume of the solid generated when the region enclosed by the given curves is revolved about the ?y-axis. ?=?^(?^2),?= sqrt 2,?=2,?=0

1) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. ?=1−?^4,?=0; about ?=2  2)  Use cylindrical shells to find the volume of the solid generated when the region enclosed by the given curves is revolved about the ?y-axis. ?=?^(?^2),?= sqrt 2,?=2,?=0

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
Section10.1: 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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1) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

?=1−?^4,?=0;

about ?=2 

2) 

Use cylindrical shells to find the volume of the solid generated when the region enclosed by the given curves is revolved about the ?y-axis.

?=?^(?^2),?= sqrt 2,?=2,?=0

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