To determine Calculate the volume of the solid generated by revolving the regions about y axis. Explanation Given information: The solid generated by revolving the region in the first quadrant bounded above by the parabola y = x 2 , below by the x -axis, and on the right by the line x = 2 . Calculation: Provide the Equation of parabola as shown below. y = x 2 x = y 1 2 Sketch the region in the first quadrant bounded above by the parabola y = x 2 , below by the x -axis, and on the right by the line x = 2 as shown in Figure 1. Refer to Figure 1. The radius R ( y ) = 2 and r ( y ) = y 1 x . The region lies between 0 to 4. Calculate the volume of the solid about x axis using the formula: V = ∫ a b π ( [ R ( y ) ] 2 − [ r ( y ) ] 2 ) d y Substitute 2 for R ( y ) , y 1 2 for r ( y ) , 0 for a , and 4 for b

University Calculus: Early Transcendentals (4th Edition)

4th Edition

ISBN: 9780134995540

Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 6.1, Problem 49E

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Calculate the volume of the solid generated by revolving the regions about y axis.

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Chapter 6.1, Problem 48E

Chapter 6.1, Problem 50E

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University Calculus: Early Transcendentals (4th Edition)

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