Find the volumes of the solids generated by revolving the region in the first quadrant bounded by the curve x = 3y - 3y³ and the y-axis about the given axes. a. The x-axis b. The line y = 1 a. The volume is (Type an exact answer in terms of .)

Find the volumes of the solids generated by revolving the region in the first quadrant bounded by the curve x = 3y - 3y³ and the y-axis about the given axes. a. The x-axis b. The line y = 1 a. The volume is (Type an exact answer in terms of .)

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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Question

2.10

Find the volumes of the solids generated by revolving the region in the first quadrant bounded by the curve
x = 3y - 3y³ and the y-axis about the given axes.
a. The x-axis
b. The line y = 1
a. The volume is
(Type an exact answer in terms of .)

Expert Solution

Step 1

$(a) x = 3 y - 3 y^{3}, a b o u t x a x i s v o l u m e (V) = \int_{a}^{b} 2 πR (y) H (y) d y w h e r e R (y) i s r a d i u s H (y) i s h e i g h t$

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