Part (a): Explanation Given: The equations are y = x , y = 2 x 1 + x 3 ; about x = − 1 . Calculation: Show the equations as below: y = 2 x 1 + x 3 (1) y = x (2) Plot a graph for the equations y = 2 x 1 + x 3 and y = x using the calculation as follows: Calculate y value using Equation (1) Substitute 0 for x in Equation (1). y = 2 ( 0 ) ( 1 + 0 3 ) = 0 Hence, the co-ordinate of ( x , y ) is ( 0 , 0 ) . Calculate y value using Equation (1) Substitute 1 for x in Equation (1). y = 2 ( 1 ) ( 1 + 1 3 ) = 2 2 = 1 Hence, the co-ordinate of ( x , y ) is ( 1 , 1 ) . Calculate y value using Equation (2) Substitute 0 for x in Equation (2). y = 0 Hence, the co-ordinate of ( x , y ) is ( 0 , 0 ) . Calculate y value using Equation (2) Substitute 1 for x in Equation (2). y = 1 Hence, the co-ordinate of ( x , y ) is ( 1 , 1 ) . Similarly calculate the coordinate values up to bound the region in the graph. Draw the cylindrical shell as shown in Figure 1. Calculate the volume using the method of cylindrical shell: V = ∫ a b 2 π x [ f ( x ) ] d x (3) Calculate the x value: Substitute ( 2 x 1 + x 3 ) for y in Equation (2) x = 2 x 1 + x 3 Part (b): To determine To evaluate: The integral function.

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 24E

Part (a):

To determine

To set up: an integral for the volume of the solid obtained by rotating the region bounded by the given curve.

Part (b):

To determine

To evaluate: The integral function.

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Chapter 6.3, Problem 23E

Chapter 6.3, Problem 25E

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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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To set up: an integral for the volume of the solid obtained by rotating the region bounded by the given curve.

Solution Summary: The author explains how to set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve.

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To set up: an integral for the volume of the solid obtained by rotating the region bounded by the given curve.

To evaluate: The integral function.

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Chapter 6 Solutions