(a) To determine Calculate the volume of the solid by revolving the region bounded by the curves along each coordinate axis using shell method. Explanation Given information: The equation of curves are y = x and y = x 2 . Calculation: Provide the equation of curve as follows. y = x (1) y = x 2 x = y 1 2 (2) Sketch the equation of curves are y = x and y = x 2 as shown in Figure 1. Refer to Figure 1. The limit along x axis is a = 0 and b = 1 . The limit along y axis is a = 0 and b = 1 . Calculate the volume about x axis as follows: The radius of the shell is y . Calculate the shell height as shown below. Shell height = y 1 2 − y Calculate the volume of the solid using shell method as shown below. V = ∫ a b 2 π ( shell radius ) ( shell height ) d y Substitute 0 for a , 1 for b , y for shell radius, and y 1 2 − y for shell height. V = ∫ 0 1 2 π ( y ) ( y 1 2 − y ) d y = 2 π ∫ 0 1 ( y 3 2 − y 2 ) d y = 2 π ( y 3 2 + 1 3 2 + 1 − y 3 3 ) 0 1 = 2 π ( 2 y 5 2 5 − y 3 3 ) 0 1 = 2 π ( 2 × 1 (b) To determine Calculate the volume of the solid by revolving the region bounded by the curves along each coordinate axis using washer method.

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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Question

Chapter 6.2, Problem 29E

(a)

To determine

Calculate the volume of the solid by revolving the region bounded by the curves along each coordinate axis using shell method.

(b)

To determine

Calculate the volume of the solid by revolving the region bounded by the curves along each coordinate axis using washer method.

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Chapter 6.2, Problem 28E

Chapter 6.2, Problem 30E

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University Calculus: Early Transcendentals (4th Edition)

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