Explanation Using Shell method, in order to evaluate the volume of the solid obtained by rotating the area between the curves y = f ( x ) and y = g ( x ) about the y -axis ( x = 0 ), where f ( x ) ≥ g ( x ) over the interval [ a , b ] is as below: V = 2 π ∫ a b x [ f ( x ) − g ( x ) ] d x Given: The following curves are given: y = x 2 and x = y 2 The axis of rotation is y -axis. Calculation: Consider the following curves: y = x 2 and x = y 2 Here, x = y 2 y = x Now, the curves are: y = x 2 and y = x The graph of the two curves is as shown below: From the graph, we see that the points of intersection are ( 0 , 0 ) and ( 1 , 1 ) ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.4, Problem 49E

To determine

The volume of the solid obtained by rotating the area between the curves $y = x^{2}$ and $x = y^{2}$ about the y-axis.

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Chapter 6.4, Problem 48E

Chapter 6.4, Problem 50E

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The volume of the solid obtained by rotating the area between the curves y = x 2 and x = y 2 about the y -axis.

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The volume of the solid obtained by rotating the area between the curves y=x2 and x=y2 about the y-axis.

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Chapter 6 Solutions

The volume of the solid obtained by rotating the area between the curves $y = x^{2}$ and $x = y^{2}$ about the y-axis.