Explanation Given: The equations are is y = e sin x and y = x 2 − 4 x + 5 . Calculation: Show the equations as below: y = e sin x (1) y = x 2 − 4 x + 5 (2) Plot a graph for the equations y = e sin x and y = x 2 − 4 x + 5 using the calculation as follows: Calculate y value using Equation (1) Substitute 0 for x in Equation (1). y = e sin 0 = 1 Hence, the co-ordinate of ( x , y ) is ( 0 , 1 ) . Calculate y value using Equation (1) Substitute 1 for x in Equation (1). y = e sin 1 = 2.32 Hence, the co-ordinate of ( x , y ) is ( 1 , 2.32 ) . Calculate y value using Equation (2) Substitute 0 for x in Equation (2). y = ( 0 ) 2 − 4 ( 0 ) + 5 = 5 The co-ordinate of ( x , y ) is ( 0 , 5 ) . Calculate y value using Equation (2). Substitute 1 for x in Equation (2). y = ( 1 ) 2 − 4 ( 1 ) + 5 = 2 The co-ordinate of ( x , y ) is ( 1 , 2 ) . Similarly calculate the coordinate values up to bound the region in the graph. Draw the region as shown in Figure 1. Refer to figure 1. The curve intersects at x 1 = 0.9 and x 2 = 2.175 . Hence, the x -coordinates are 0.9, 2.175. Therefore, the x -coordinates of the points of intersection of the curves are 0.9, 2.175. Calculate the volume using the method of cylindrical shell: V = ∫ a b 2 π x [ f ( x ) ] d x (3) Consider f ( x ) = y − ( x 2 − 4 x + 5 ) (4) Substitute ( e sin x ) for y in Equation (4). f ( x ) = ( e sin x ) − ( x 2 − 4 x + 5 ) Substitute 0.9 for a , 2.175 for b , and [ ( e sin x ) − ( x 2 − 4 x + 5 ) ] for [ f ( x ) ] in Equation (3). V = ∫ 0.9 2.175 2 π x [ ( e sin x ) − ( x 2 − 4 x + 5 ) ] d x = 2 π ∫ 0.9 2.175 [ x e sin x − ( x 3 − 4 x 2 + 5 x ) ] d x = 2 π ∫ 0.9 2.175 ( x e sin x ) d x − 2 π ∫ 0

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ISBN: 9781305266636

Author: James Stewart

Publisher: Cengage Learning

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Chapter 5.3, Problem 34E

To determine

To estimate: The x-coordinates of the points of intersection of the curves by using the graph.

To estimate: The volume of the solid obtained by rotating about the y-axis the region enclosed by the curves.

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Chapter 5.3, Problem 33E

Chapter 5.3, Problem 35E

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To estimate: The x -coordinates of the points of intersection of the curves by using the graph. To estimate: The volume of the solid obtained by rotating about the y -axis the region enclosed by the curves.

Solution Summary: The author explains how to estimate the x -coordinates of the points of intersection of curves by using the graph.

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To estimate: The x-coordinates of the points of intersection of the curves by using the graph.

To estimate: The volume of the solid obtained by rotating about the y-axis the region enclosed by the curves.

Want to see the full answer?

Chapter 5 Solutions

To estimate: The x -coordinates of the points of intersection of the curves by using the graph. To estimate: The volume of the solid obtained by rotating about the y -axis the region enclosed by the curves.

Solution Summary: The author explains how to estimate the x -coordinates of the points of intersection of curves by using the graph.

Concept explainers

Videos

To estimate: The x-coordinates of the points of intersection of the curves by using the graph. To estimate: The volume of the solid obtained by rotating about the y-axis the region enclosed by the curves.

Want to see the full answer?

Chapter 5 Solutions

To estimate: The x-coordinates of the points of intersection of the curves by using the graph.

To estimate: The volume of the solid obtained by rotating about the y-axis the region enclosed by the curves.