Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y=8x³, y=0, x= 1; about x=2 V= 64x X

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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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = 8x³, y=0, x= 1; about x = 2
V=
-0.3
64x
Sketch the region.
y
-0.5
O
10
X
8
x
0.5 1.0 1.5 20 2.5
0.5 1.0 1.5 2.0 2.5
-0.5
GO
0.5
9
1.5 2.0
-0.5
GO
0.5
1.0 1.5 2,0
2.5
Transcribed Image Text:Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 8x³, y=0, x= 1; about x = 2 V= -0.3 64x Sketch the region. y -0.5 O 10 X 8 x 0.5 1.0 1.5 20 2.5 0.5 1.0 1.5 2.0 2.5 -0.5 GO 0.5 9 1.5 2.0 -0.5 GO 0.5 1.0 1.5 2,0 2.5
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