Explanation Obtain the radius and height of the solid graphically and use it to calculate the volume by the Shell Method. Given: f ( x ) = a − x with a > 0 [ 0 , a ] about x = − 1 Calculation: The graph of the solid is shown below: Each shell has radius x + 1 and height a − x . The volume of the solid thus obtained is given by 2 π ∫ 0 a ( x + 1 ) ( a − x ) d x = 2 π ∫ 0 a ( a

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.4, Problem 19E

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 18E

Chapter 6.4, Problem 20E

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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