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Find the volume generated by revolving the region bounded by y = x2, y = 0, and x = 2 about the following. (a) the x-axis 6.4n units3 (b) the line y = -2 3767 X units3 15 (c) the line x = 3 12T X units3 Recall the volume of a solid generated by a region bounded by f(x) on the interval [a, b] rotated about the x-axis is given by V = A which is called the "disk" method. Also recall that the volume of the solid obtained by rotating the region between two functions r, and r, satisfying r, > r, on the interval [a, b] about the x-axis is given by V = A (r, 2 - r,2)dx where r, represents the outer radius and r, represents the inner radius and this is called the "washer" method. Make a sketch of the bounded region and revolve it about each given line, the axis of revolution. The radius is measured from the axis of revolution to the function. Does the figure represent a "disk" or a "washer"? How is the length of the radius affected if the axis of revolution is a line other than the x-axis?

Find the volume generated by revolving the region bounded by y = x2, y = 0, and x = 2 about the following. (a) the x-axis 6.4n units3 (b) the line y = -2 3767 X units3 15 (c) the line x = 3 12T X units3 Recall the volume of a solid generated by a region bounded by f(x) on the interval [a, b] rotated about the x-axis is given by V = A which is called the "disk" method. Also recall that the volume of the solid obtained by rotating the region between two functions r, and r, satisfying r, > r, on the interval [a, b] about the x-axis is given by V = A (r, 2 - r,2)dx where r, represents the outer radius and r, represents the inner radius and this is called the "washer" method. Make a sketch of the bounded region and revolve it about each given line, the axis of revolution. The radius is measured from the axis of revolution to the function. Does the figure represent a "disk" or a "washer"? How is the length of the radius affected if the axis of revolution is a line other than the x-axis?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find the volume generated by revolving the region bounded by y = x2, y = 0, and x = 2 about the following. (a) the x-axis 6.4n units3 (b) the line y = -2 3767 X units3 15 (c) the line x = 3 12T X units3 Recall the volume of a solid generated by a region bounded by f(x) on the interval [a, b] rotated about the x-axis is given by V = A which is called the "disk" method. Also recall that the volume of the solid obtained by rotating the region between two functions r, and r, satisfying r, > r, on the interval [a, b] about the x-axis is given by V = A (r, 2 - r,2)dx where r, represents the outer radius and r, represents the inner radius and this is called the "washer" method. Make a sketch of the bounded region and revolve it about each given line, the axis of revolution. The radius is measured from the axis of revolution to the function. Does the figure represent a "disk" or a "washer"? How is the length of the radius affected if the axis of revolution is a line other than the x-axis?
Transcribed Image Text:Find the volume generated by revolving the region bounded by y = x2, y = 0, and x = 2 about the following. (a) the x-axis 6.4n units3 (b) the line y = -2 3767 X units3 15 (c) the line x = 3 12T X units3 Recall the volume of a solid generated by a region bounded by f(x) on the interval [a, b] rotated about the x-axis is given by V = A which is called the "disk" method. Also recall that the volume of the solid obtained by rotating the region between two functions r, and r, satisfying r, > r, on the interval [a, b] about the x-axis is given by V = A (r, 2 - r,2)dx where r, represents the outer radius and r, represents the inner radius and this is called the "washer" method. Make a sketch of the bounded region and revolve it about each given line, the axis of revolution. The radius is measured from the axis of revolution to the function. Does the figure represent a "disk" or a "washer"? How is the length of the radius affected if the axis of revolution is a line other than the x-axis?
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