Explanation Obtain the radius and height of the solid graphically and use it to calculate the volume by the Shell Method. Given: f ( x ) = 1 − x 2 [ − 1 , 1 ] , x = c with c > 1 Calculation: The graph of the solid is shown below: Each shell has radius c − x and height 1 − x 2 . The volume of the solid thus obtained is given by 2 π ∫ − 1 1 ( 1 − x 2 ) ( c − x ) d x = 2 π ∫ − 1 1

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 6.4, Problem 20E

To determine

The volume of the solid obtained by rotating the region underneath the graph of $f$ over the interval about the given axis after sketching it, by using the Shell Method.

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Chapter 6.4, Problem 19E

Chapter 6.4, Problem 21E

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The volume of the solid obtained by rotating the region underneath the graph of f over the interval about the given axis after sketching it, by using the Shell Method.

Solution Summary: The author explains how to determine the volume of the solid obtained by rotating the region underneath the graph of f over the interval about the given axis.

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The volume of the solid obtained by rotating the region underneath the graph of $f$ over the interval about the given axis after sketching it, by using the Shell Method.

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Chapter 6 Solutions