(a) Explanation Given information: The equation of curves are y = x 4 and y = 4 − 3 x 2 . The equation of the line is x = 1 . Calculation: Provide the equation of curve as follows. y = x 4 (1) y = 4 − 3 x 2 (2) The limits are a = − 1 and b = 1 . The radius of the shell is ( 1 − x ) . Calculate the shell height as shown below. Shell height = 4 − 3 x 2 − x 4 Calculate the volume of the solid using shell method as shown below. V = ∫ a b 2 π ( shell radius ) ( shell height ) d x Substitute − 1 for a , 1 for b , 1 − x for shell radius, and 4 − 3 x 2 − x 4 for shell height. V = ∫ − 1 1 2 π ( 1 − x ) ( 4 − 3 x 2 − x 4 ) d x = 2 π ∫ − 1 1 ( 4 − 3 x 2 − x 4 − 4 x + 3 x 3 − x 5 ) d x = 2 π ( 4 x − 3 x 3 3 − (b) To determine Calculate the volume of the solid by revolving the region bounded by the curves along x axis using shell method.

Thomas' Calculus: Early Transcendentals, Single Variable (14th Edition)

14th Edition

ISBN: 9780134439419

Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher: PEARSON

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Chapter 6.2, Problem 26E

(a)

To determine

Calculate the volume of the solid by revolving the region bounded by the curves along the line x=1 using shell method.

(b)

To determine

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

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Chapter 6.2, Problem 25E

Chapter 6.2, Problem 27E

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Thomas' Calculus: Early Transcendentals, Single Variable (14th Edition)

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Calculate the volume of the solid by revolving the region bounded by the curves along the line x = 1 using shell method.