Explanation Given: The functions are y = x 2 − 1 , y = 2 x − 1 , and axis x = − 2 . Formula used: Volume V = ∫ a b A ( x ) d x Where a ≤ x ≤ b and A = 2 π r h . Calculation: The functions are y = x 2 − 1 , y = 2 x − 1 , and axis x = − 2 . The graphs of y = x 2 − 1 and y = 2 x − 1 intersect where x 2 − 1 = 2 x − 1 x 2 − 1 − 2 x + 1 = 0 x 2 − 2 x = 0 Find the factors if the above equation. x 2 − 2 x = 0 x ( x − 2 ) = 0 That is, x = 0 or ( x − 2 ) = 0 x = 0 or x = 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 y = x 2 − 1 and y = 2 x − 1 verticallyover the interval [ 0 , 2 ] . This vertical slice is parallel to the axis of rotation. Now, use the shell method to calculate the volume of the solid. For each x ∈ [ 0 , 2 ] , the shell with radius x − ( − 2 ) = x + 2 and height ( 2 x − 1 ) − ( x 2 − 1 ) = 2 x − x 2 ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6, Problem 33CRE

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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 32CRE

Chapter 6, Problem 34CRE

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Chapter 6 Solutions

Calculus - Standalone book

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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