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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F638d3a15-e6c8-4dbb-af03-e006d7a575bc%2F9974a30c-ee06-4b0f-b767-c92b3798ce84%2F97mz997_processed.jpeg&w=3840&q=75)
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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