Explanation Given: The functions are y = x 2 + 2 , y = x + 4 , and x − axis . 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 + 2 , y = x + 4 , and x − axis . The graphs of y = x 2 + 2 and y = x + 4 intersect where x 2 + 2 = x + 4 x 2 + 2 − x − 4 = 0 x 2 − x − 2 = 0 Find the factors of the above equation. x 2 − 2 x + x − 2 = 0 x ( x − 2 ) + 1 ( x − 2 ) = 0 ( x − 2 ) ( x + 1 ) = 0 That is. ( x − 2 ) = 0 or ( x + 1 ) = 0 x = 2 or x = − 1 The graph of the function is: Thus, the enclosed area lies over the interval [ − 1 , 2 ] . Choose the slice of region bounded by the graphs y = x 2 + 2 and y = x + 4 vertically over the interval [ − 1 , 2 ] . 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 , 2 ] , the washer with outer radius R = x + 4 and inner radius r = x 2 + 2 . Now, find the volume...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 6, Problem 29CRE

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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 28CRE

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Chapter 6 Solutions

CALCULUS (CLOTH)

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

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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