Explanation Given: The functions are x = 4 y − y 3 , x = 0 , y ≥ 0 and x − axis . 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 = 4 y − y 3 , x = 0 , y ≥ 0 and x − axis . The graphs of x = 4 y − y 3 and x = 0 intersect where 4 y − y 3 = 0 Find the factors of the above equation. y ( 4 − y 2 ) = 0 y ( 2 − y ) ( 2 + y ) = 0 That is. y = 0 or ( 2 − y ) = 0 or ( 2 + y ) = 0 y = 0 or y = 2 or y = − 2 But y ≥ 0 , so points are y = 0 or y = 2 . The graph of the function is: Thus, the enclosed area lies over the interval [ 0 , 2 ] . Choose the slice of region bounded by the graphs x = 4 y − y 3 and x = 0 horizontally over the interval [ 0 , 2 ] ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6, Problem 37CRE

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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 36CRE

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

Solution Summary: The author calculates the volume of the solid obtained by rotating the region enclosed by the curves about the given axis.

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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 Solutions