Explanation Given: The equation about the y -axis is x 2 + ( y − 1 ) 2 = 1 Calculation: Show the equation as below: x 2 + ( y − 1 ) 2 = 1 (1) Plot a graph for the equation x 2 + ( y − 1 ) 2 = 1 using the calculation as follows: Calculate x value using Equation (1). Substitute 0 for y in Equation (1). x 2 + ( 0 − 1 ) 2 = 1 x 2 = 1 − 1 x = 0 Hence, the co-ordinate of ( x , y ) is ( 0 , 0 ) . Calculate x value using Equation (1) Substitute 1 for y in Equation (1). x 2 + ( 1 − 1 ) 2 = 1 x 2 = 1 x = 1 = ± 1 Hence, the co-ordinate of ( x , y ) is ( 1 , ± 1 ) . Calculate x value using Equation (1) Substitute 2 for y in Equation (1). x 2 + ( 2 − 1 ) 2 = 1 x 2 = 1 − 1 x = 0 The co-ordinate of ( x , y ) is ( 2 , 0 ) . Draw the disk as shown in Figure 1. Calculate the volume using the method of disk: V = ∫ a b π [ f ( y ) ] 2 d y (2) Rearrange the Equation (1). x 2 = 1 − ( y − 1 ) 2 x = 1 − ( y − 1 ) 2 Substitute0for a , 2 for b , and 1 − ( y − 1 ) 2 for [ f ( y ) ] in Equation (2)

Single Variable Calculus: Early Transcendentals, Volume I

8th Edition

ISBN: 9781305270343

Author: James Stewart

Publisher: Cengage Learning

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Chapter 6.3, Problem 41E

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To find: The volume of the resulting solid by the region bounded by given curve using the method of disk.

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Chapter 6.3, Problem 40E

Chapter 6.3, Problem 42E

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Chapter 6 Solutions

Single Variable Calculus: Early Transcendentals, Volume I

Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Sketch the region enclosed by the given curves....

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The volume of the resulting solid by the region bounded by given curve using the method of disk.

Solution Summary: The author calculates the volume of the resulting solid by the region bounded by given curve using the method of disk.

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To find: The volume of the resulting solid by the region bounded by given curve using the method of disk.

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Chapter 6 Solutions