Explanation Given: The functions are y 2 = x − 1 , x = 1 , x = 3 and axis y = − 3 . 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 2 = x − 1 , x = 1 , x = 3 and axis y = − 3 . The points are 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 2 = x − 1 , x = 1 and 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 = 1 x − ( − 3 ) = 3 + 1 x and inner radius r = − 1 x − ( − 3 ) = 3 − 1 x . 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 38CRE

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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 37CRE

Chapter 6, Problem 39CRE

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Find the volume of the solid obtained by rotating the region enclosed by the curves y = 32 x2 y = 2 +1– x²| about - y = 25. (Use symbolic notation and fractions where needed.) Volume =| %3D

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Determine the volume of the solid formed by rotation about the y-axis of the region bounded by the curve y = 9 In x, the x-axis, the y-axis and the line y=9 In22. 30 25 20 15 10 5. -25 -20 -15 -10 -5 10 15 20 25 Volume of the solid is 3 units

Chapter 6 Solutions

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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 explains how to determine 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