Explanation Given: The functions are x = y 2 − 3 , x = 2 y , and axis y = 4 . Formula used: Volume V = ∫ c d A ( y ) d y Where c ≤ y ≤ d and A = 2 π r h . Calculation: The functions are x = y 2 − 3 , x = 2 y , and axis y = 4 . The graphs of x = y 2 − 3 and x = 2 y intersect where y 2 − 3 = 2 y y 2 − 3 − 2 y = 0 y 2 − 2 y − 3 = 0 Find the factors of the above equation. y 2 − 3 y + y − 3 = 0 y ( y − 3 ) + 1 ( y − 3 ) = 0 ( y − 3 ) ( y + 1 ) = 0 That is. ( y − 3 ) = 0 or ( y + 1 ) = 0 y = 3 or y = − 1 The graph of the function is: Thus, the enclosed area lies over the interval [ − 1 , 3 ] . Choose the slice of region bounded by the graphs x = y 2 − 3 and x = 2 y horizontally over the interval [ − 1 , 3 ] . This horizontal slice is parallel to the axis of rotation. Now, use the shell method to calculate the volume of the solid. For each y ∈ [ − 1 , 3 ] , the shell with radius 4 − y and height 2 y − ( y 2 − 3 ) = 3 + 2 y − y 2 ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6, Problem 31CRE

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Find the volume of the solid obtained by rotating the region enclosed by the curves about the given axis.

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Chapter 6, Problem 30CRE

Chapter 6, Problem 32CRE

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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

Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - 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