A solid is obtained by rotating the shaded region about the specified line. about the x-axis V = y 5 4 3 2 1 y=√x 5 2TY 10 y = 12 - x (a) Set up an integral using the method of cylindrical shells for the volume of the solid. 3 6²³ 15 dy X (b) Evaluate the integral to find the volume of the solid.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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A solid is obtained by rotating the shaded region about the specified line.
about the x-axis
V =
y
5
4
3
2
1
y=√x
5
10
y = 12 - x
15
(a) Set up an integral using the method of cylindrical shells for the volume of the solid.
3
-6²³
2πy|
/0
dy
X
(b) Evaluate the integral to find the volume of the solid.
Transcribed Image Text:A solid is obtained by rotating the shaded region about the specified line. about the x-axis V = y 5 4 3 2 1 y=√x 5 10 y = 12 - x 15 (a) Set up an integral using the method of cylindrical shells for the volume of the solid. 3 -6²³ 2πy| /0 dy X (b) Evaluate the integral to find the volume of the solid.
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