In Exercises 23-26, use the shell method to find the volumes of the solids generated by revolving the regions bounded by the given curves about the given lines. 23. y = 3x, y = 0, x = 2 a. The y-axis b. The line x = 4

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Chapter2: Second-order Linear Odes
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Exercise 23 - 25

Revolution About the x-Axis
Use the shell method to find the volumes of the solids generated by re-
volving the regions bounded by the curves and lines in Exercises
15-22 about the x-axis.
15. х %3D Vy, х %3D —у, у3 2
16. х %3D у?, х%3D - у, у3 2, у30
17. x = 2y – y, x = 0
18. x = 2y – y?,
x = y
19. у %3D x], у%3D 1
20. у %3D х, у%3D 2х, у %3D 2
21. у 3 Vx, у %3D0, у-х— 2
22. у 3D Vx, у%3D 0, у%3D 2 — х
Revolution About Horizontal and Vertical Lines
In Exercises 23–26, use the shell method to find the volumes of the
solids generated by revolving the regions bounded by the given curves
about the given lines.
23. у %3D 3х, у %3D 0, х%3D2
a. The y-axis
c. The line x = -1
e. The line y = 7
24. y = x', y = 8, x = 0
b. The line x = 4
d. The x-axis
f. The line y = -2
b. The line x = 3
d. The x-axis
f. The line y = -1
a. The y-axis
c. The line x = -2
e. The line y = 8
25. y = x + 2, y= x?
b. The line x = -1
d. The line y = 4
a. The line x = 2
c. The x-axis
Transcribed Image Text:Revolution About the x-Axis Use the shell method to find the volumes of the solids generated by re- volving the regions bounded by the curves and lines in Exercises 15-22 about the x-axis. 15. х %3D Vy, х %3D —у, у3 2 16. х %3D у?, х%3D - у, у3 2, у30 17. x = 2y – y, x = 0 18. x = 2y – y?, x = y 19. у %3D x], у%3D 1 20. у %3D х, у%3D 2х, у %3D 2 21. у 3 Vx, у %3D0, у-х— 2 22. у 3D Vx, у%3D 0, у%3D 2 — х Revolution About Horizontal and Vertical Lines In Exercises 23–26, use the shell method to find the volumes of the solids generated by revolving the regions bounded by the given curves about the given lines. 23. у %3D 3х, у %3D 0, х%3D2 a. The y-axis c. The line x = -1 e. The line y = 7 24. y = x', y = 8, x = 0 b. The line x = 4 d. The x-axis f. The line y = -2 b. The line x = 3 d. The x-axis f. The line y = -1 a. The y-axis c. The line x = -2 e. The line y = 8 25. y = x + 2, y= x? b. The line x = -1 d. The line y = 4 a. The line x = 2 c. The x-axis
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