Explanation Determine the radius of the disk obtained by the rotation of the given region and use this to determine the volume of the solid thus obtained by assuming u = f ( x ) . Given: The curve y = f ( x ) in Figure 18, called a tractrix, has the following property: The tangent line at each point ( x , y ) on the curve has the slope d y d x = − y 1 − y 2 . R is the shaded region under the graph of y = f ( x ) for 0 ≤ x ≤ a in Figure 18. Also given a hint that we need to use the substitution u = f ( x ) to show that V = π ∫ c 1 u 1 − u 2 d u Calculation: Let y = f ( x ) be the curve given. Rotating the region R about the x -axis produces a solid whose cross-sections are disks with radius f ( x ) ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.3, Problem 62E

To determine

The volume $V$ of the solid obtained by revolving $R$ around the $x$ -axis in terms of the constant $c = f (a)$ .

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Chapter 6.3, Problem 61E

Chapter 6.3, Problem 63E

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Chapter 6 Solutions

Calculus - Standalone book

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The volume V of the solid obtained by revolving R around the x -axis in terms of the constant c = f ( a ) .

Solution Summary: The author explains how to determine the volume of the solid obtained by revolving R around the x -axis.

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The volume $V$ of the solid obtained by revolving $R$ around the $x$ -axis in terms of the constant $c = f (a)$ .

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Chapter 6 Solutions

The volume V of the solid obtained by revolving R around the x -axis in terms of the constant c = f ( a ) .

Solution Summary: The author explains how to determine the volume of the solid obtained by revolving R around the x -axis.

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The volume V of the solid obtained by revolving R around the x-axis in terms of the constant c=f(a).

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Chapter 6 Solutions

The volume $V$ of the solid obtained by revolving $R$ around the $x$ -axis in terms of the constant $c = f (a)$ .