Tutorial Exercise Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = x² x=0 y = 36 Step 1

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 41E: Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed...
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Tutorial Exercise
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis.
y = x²
x=0
y = 36
Step 1
Because the axis of revolution is horizontal, use a horizontal
Step 2
Consider a representative rectangle as shown in the figure.
y
35
30-
25
20
15
10
5-
0
1 2 3
4 5 6
The width Ay indicates that y is the variable of integration.
horizontal representative rectangle.
The distance from the center of the rectangle to the axis of revolution is p(y) = x
x
and the height of the rectangle is h(y) = x
Transcribed Image Text:Tutorial Exercise Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = x² x=0 y = 36 Step 1 Because the axis of revolution is horizontal, use a horizontal Step 2 Consider a representative rectangle as shown in the figure. y 35 30- 25 20 15 10 5- 0 1 2 3 4 5 6 The width Ay indicates that y is the variable of integration. horizontal representative rectangle. The distance from the center of the rectangle to the axis of revolution is p(y) = x x and the height of the rectangle is h(y) = x
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