#12 only Use the shell method to find the volume of the solid of revolution for the region generatedby 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 exactanswer (NOT A DECIMAL).11. Rotating around a horizontal axis: xy 1,x 0, y = 1, y = 3 and rotated abouty = -1.12. Rotating around a vertical axis: y = 4x – x2, y = 3 and rotated about x = 1.

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#12 only

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

#12 only

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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