Explanation Given: The functions are y = − x 2 + 4 x − 3 , y = 0 , and axis x = 4 . 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 + 4 x − 3 , y = 0 , and axis x = 4 . 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 parallel to the axis of rotation. Now, use the shell method to calculate the volume of the solid. For each x ∈ [ 1 , 3 ] , the shell with radius 4 − x and height − x 2 + 4 x − 3 . Now, find the volume...

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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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.

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Chapter 6, Problem 35CRE

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Prob. 48E Ch. 6.4 - Prob. 49E Ch. 6.4 - Prob. 50E Ch. 6.4 - Prob. 51E Ch. 6.4 - Prob. 52E Ch. 6.4 - Prob. 53E Ch. 6.4 - Prob. 54E Ch. 6.4 - Prob. 55E Ch. 6.4 - Prob. 56E Ch. 6.4 - Prob. 57E Ch. 6.4 - Prob. 58E Ch. 6.4 - Prob. 59E Ch. 6.4 - Prob. 60E Ch. 6.4 - Prob. 61E Ch. 6.4 - Prob. 62E Ch. 6.4 - Prob. 63E Ch. 6.4 - Prob. 64E Ch. 6.5 - Prob. 1PQ Ch. 6.5 - Prob. 2PQ Ch. 6.5 - Prob. 3PQ Ch. 6.5 - Prob. 4PQ Ch. 6.5 - Prob. 1E Ch. 6.5 - Prob. 2E Ch. 6.5 - Prob. 3E Ch. 6.5 - Prob. 4E Ch. 6.5 - Prob. 5E Ch. 6.5 - Prob. 6E Ch. 6.5 - Prob. 7E Ch. 6.5 - Prob. 8E Ch. 6.5 - Prob. 9E Ch. 6.5 - Prob. 10E Ch. 6.5 - Prob. 11E Ch. 6.5 - Prob. 12E Ch. 6.5 - Prob. 13E Ch. 6.5 - Prob. 14E Ch. 6.5 - Prob. 15E Ch. 6.5 - Prob. 16E Ch. 6.5 - Prob. 17E Ch. 6.5 - Prob. 18E Ch. 6.5 - Prob. 19E Ch. 6.5 - Prob. 20E Ch. 6.5 - Prob. 21E Ch. 6.5 - Prob. 22E Ch. 6.5 - Prob. 23E Ch. 6.5 - Prob. 24E Ch. 6.5 - Prob. 25E Ch. 6.5 - Prob. 26E Ch. 6.5 - Prob. 27E Ch. 6.5 - Prob. 28E Ch. 6.5 - Prob. 29E Ch. 6.5 - Prob. 30E Ch. 6.5 - 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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