Explanation Given information: The given curves are y = x 2 + 2 , y = ( x − 2 ) 2 and the x-axis and y-axis which is rotated about x-axis. Concept Used: We use the concept of Disk method. If f is continuous and f ( x ) ≥ 0 on [ a , b ] , then the solid obtained by rotating the region under the graph about the x-axis has volume (with R=f(x )) V = π ∫ a b ( f ( x ) ) 2 d x Calculation: As given curves are y = x 2 + 2 , y = ( x − 2 ) 2 which is rotated about x -axis, we find the point of intersections by x 2 + 2 = ( x − 2 ) 2 x 2 + 2 = x 2 − 4 x + 4 2 = − 4 x + 4 2 − 4 = − 4 x − 2 = − 4 x x = 1 2 Now, as we rotate about the x-axis, two different cross-sections are obtained from 0 ≤ x ≤ 1 2 and 1 2 ≤ x ≤ 2 . Thus, the volume is given by V = π ∫ 0 1 2 ( x 2 + 2 ) 2 d x + π ∫ 1 2 2 ( (

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.3, Problem 26E

To determine

The volume of the solid obtained by rotating the region R about the x -axis.

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Chapter 6.3, Problem 25E

Chapter 6.3, Problem 27E

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Chapter 6 Solutions

Calculus - Standalone book

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The volume of the solid obtained by rotating the region R about the x -axis.

Solution Summary: The author calculates the volume of the solid obtained by rotating the region R about the x-axis.

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The volume of the solid obtained by rotating the region R about the x -axis.

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Chapter 6 Solutions