Explanation The sketch of the solid obtained by rotation is determined and then we use the Shell Method to obtain its volume after calculating its height and radius. Given: f ( x ) = x x 3 + 1 over the interval [ 1 , 4 ] . Calculation: The sketch of the solid obtained is shown below: The shell has radius x and height x x 3 + 1 therefore the volume of the solid is given by 2 π ∫ 1 4 x ( x x 3 + 1 ) d x ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.4, Problem 6E

To determine

To sketch the solid obtained by rotating the region underneath the graph of the function over the given interval about the $y$ -axis and also find its volume.

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Chapter 6.4, Problem 5E

Chapter 6.4, Problem 7E

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Chapter 6 Solutions

Calculus - Standalone book

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

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To sketch the solid obtained by rotating the region underneath the graph of the function over the given interval about the y -axis and also find its volume.

Solution Summary: The author explains how the sketch of the solid obtained by rotation is determined and then uses the Shell Method to obtain its volume.

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To sketch the solid obtained by rotating the region underneath the graph of the function over the given interval about the $y$ -axis and also find its volume.

Want to see the full answer?

Chapter 6 Solutions

To sketch the solid obtained by rotating the region underneath the graph of the function over the given interval about the y -axis and also find its volume.

Solution Summary: The author explains how the sketch of the solid obtained by rotation is determined and then uses the Shell Method to obtain its volume.

Concept explainers

Videos

To sketch the solid obtained by rotating the region underneath the graph of the function over the given interval about the y-axis and also find its volume.

Want to see the full answer?

Chapter 6 Solutions

To sketch the solid obtained by rotating the region underneath the graph of the function over the given interval about the $y$ -axis and also find its volume.