Explanation Given: The equation is y = − x 2 + 6 x − 8 , y = 0 , about the y -axis. Calculation: Show the equation as below: y = − x 2 + 6 x − 8 (1) Plot a graph for the equation y = − x 2 + 6 x − 8 using the calculation as follows: Calculate y value using Equation (1) Substitute 0 for x in Equation (1). y = − 0 2 + 6 ( 0 ) − 8 y = 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 = − 1 2 + 6 ( 1 ) − 8 = − 1 + 6 − 8 = − 3 Hence, the co-ordinate of ( x , y ) is ( 1 , − 3 ) . Calculate y value using Equation (1) Substitute 2 for x in Equation (1). y = − 2 2 + 6 ( 2 ) − 8 = − 4 + 12 − 8 = 0 The co-ordinate of ( x , y ) is ( 2 , 0 ) . Calculate y value using Equation (1) Substitute 3 for x in Equation (1). y = − 3 2 + 6 ( 3 ) − 8 = − 9 + 18 − 8 = 1 The co-ordinate of ( x , y ) is ( 3 , 1 ) . Calculate y value using Equation (1) Substitute 4 for x in Equation (1). y = − 4 2 + 6 ( 4 ) − 8 = − 16 + 24 − 8 = 0 The co-ordinate of ( x , y ) is ( 4 , 0 ) . Draw the shell as Figure 1. Calculate the volume using the method of cylindrical shell: V = ∫ a b 2 π x [ f ( x ) ] d x (2) Substitute 2 for a , 4 for b , and ( − x 2 + 6 x − 8 ) for [ f ( x ) ] in Equation (2)

8th Edition

ISBN: 9789814875608

Author: Stewart

Publisher: VST

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Chapter 6.3, Problem 37E

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To find: The volume of the resulting solid by method of cylindrical shell.

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EBK SINGLE VARIABLE CALCULUS: EARLY TRA

Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.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 - Prob. 7E Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

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The volume of the resulting solid by method of cylindrical shell.

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To find: The volume of the resulting solid by method of cylindrical shell.

Chapter 6 Solutions