Explanation After sketching the enclosed region, the volume of the solid obtained by rotation about the x -axis is calculated by the Shell Method, after determining the radius and height of the solid. Given: y = ( 4 − x 2 ) , x = 0 , y = 0 Calculation: The sketch of the region y = ( 4 − x 2 ) , x = 0 , y = 0 is given below: When this region is rotated about the x -axis, each shell has radius y and height 4 − y , hence the volume of the resulting solid is given by 2 π ∫ 0 4 y ( 4 − y ) d y Assumi...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.4, Problem 25E

To determine

The sketch of the enclosed region and use the Shell Method to calculate the volume of rotation about the $x$ -axis.

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Chapter 6.4, Problem 24E

Chapter 6.4, Problem 26E

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Chapter 6 Solutions

Calculus - Standalone book

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The sketch of the enclosed region and use the Shell Method to calculate the volume of rotation about the x -axis.

Solution Summary: The author calculates the volume of the solid obtained by rotation about the x -axis by using the Shell Method.

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The sketch of the enclosed region and use the Shell Method to calculate the volume of rotation about the $x$ -axis.

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Chapter 6 Solutions

The sketch of the enclosed region and use the Shell Method to calculate the volume of rotation about the x -axis.

Solution Summary: The author calculates the volume of the solid obtained by rotation about the x -axis by using the Shell Method.

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The sketch of the enclosed region and use the Shell Method to calculate the volume of rotation about the x-axis.

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Chapter 6 Solutions

The sketch of the enclosed region and use the Shell Method to calculate the volume of rotation about the $x$ -axis.