Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = and y = 0. (a) A typical shell has radius x, circumference 2πx, and height f(x): (b) So, by the shell method, the volume is = 5² 0 and a = = V = (c) Evaluate the integral: V = dx 9x²x³

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 6E: Suppose that r=12 cm and h=15 cm in the right circular cylinder. Find the exact and approximate a...
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Find the volume of the solid obtained by rotating about the y-axis the region bounded by y =
and y = 0.
(a) A typical shell has radius x, circumference 2πx,
and height f(x):
(b)
So, by the shell method, the volume is
= 5²
0
and a =
=
V =
(c) Evaluate the integral: V =
dx
9x²x³
Transcribed Image Text:Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = and y = 0. (a) A typical shell has radius x, circumference 2πx, and height f(x): (b) So, by the shell method, the volume is = 5² 0 and a = = V = (c) Evaluate the integral: V = dx 9x²x³
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