Explanation Given: The functions are y = − x 2 + 4 x − 3 , y = 0 , and axis y = − 1 . Formula used: Volume V = ∫ a b A ( x ) d x Where a ≤ x ≤ b and A = π [ ( Outer radius ) 2 − ( Inner radius ) 2 ] . Calculation: The functions are y = − x 2 + 4 x − 3 , y = 0 , and axis y = − 1 . The graphs of y = − x 2 + 4 x − 3 and y = 0 intersect where − x 2 + 4 x − 3 = 0 x 2 − 4 x + 3 = 0 Find the factors of the above equation. x 2 − 3 x − x + 3 = 0 x ( x − 3 ) − 1 ( x − 3 ) = 0 ( x − 1 ) ( x − 3 ) = 0 That is. ( x − 1 ) = 0 or ( x − 3 ) = 0 x = 1 or x = 3 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 y = − x 2 + 4 x − 3 vertically over the interval [ 1 , 3 ] . This vertical slice is perpendicular to the axis of rotation. Now, use the washer method to calculate the volume of the solid. For each x ∈ [ 1 , 3 ] , the washer with outer radius R = − x 2 + 4 x − 3 − ( − 1 ) = − x 2 + 4 x − 2 and inner radius r = 0 − ( − 1 ) = 1 . Now, find the volume...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6, Problem 35CRE

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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 34CRE

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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