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2. Rotating around a vertical axis: y = 4x -x2, y = 3 and rotated about x = 1.

2. Rotating around a vertical axis: y = 4x -x2, y = 3 and rotated about x = 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use the shell method to find the volume of the solid of revolution for the region generated by the two curves when the region is rotated around the given axis. a. Find the points of intersection and limits for your integral. b. Graph the region. Shade the region that will be rotated. c. Set up the integral and simplify the function. d. Find the value of the definite integral. Show all of your work. Write an exact answer (NOT A DECIMAL). 11. Rotating around a horizontal axis: xy 1,x 0, y = 1, y = 3 and rotated about y = -1. 12. Rotating around a vertical axis: y = 4x – x2, y = 3 and rotated about x = 1.
Transcribed Image Text:Use the shell method to find the volume of the solid of revolution for the region generated by the two curves when the region is rotated around the given axis. a. Find the points of intersection and limits for your integral. b. Graph the region. Shade the region that will be rotated. c. Set up the integral and simplify the function. d. Find the value of the definite integral. Show all of your work. Write an exact answer (NOT A DECIMAL). 11. Rotating around a horizontal axis: xy 1,x 0, y = 1, y = 3 and rotated about y = -1. 12. Rotating around a vertical axis: y = 4x – x2, y = 3 and rotated about x = 1.
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