Explanation Graphically represent the given region and determine if vertical slicing is or horizontal slicing simpler. Based on the analysis, the volume of the solid can be conveniently calculated. Given: Region in Figure 13 is rotated about the y -axis Calculation: From the sketch, if the indicated region is sliced vertically, the top of the slice will lie along the curve y = x − x 12 and the bottom will lie along the curve y = 0 . If slice horizontally, the equation must be solved for x to determine the endpoints. So it will be easier to slice it vertically. We will hence use Shell Method as it will be helpful in cases where the vertical slice is parallel to the axis of rotation. Each shell has radius x and height x − x 12 ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 6.4, Problem 54E

To determine

The volume of rotation using the most convenient method among Disk and Shell methods, about the region specified.

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Chapter 6.4, Problem 53E

Chapter 6.4, Problem 55E

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CALCULUS (CLOTH)

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The volume of rotation using the most convenient method among Disk and Shell methods, about the region specified.

Solution Summary: The author explains how the volume of the solid obtained by rotation, determined by Shell Method, is found to be 11 21.

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The volume of rotation using the most convenient method among Disk and Shell methods, about the region specified.

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Chapter 6 Solutions