a. Explanation Given: The curves are y = x 1 n and y = x n . The region is revolved about the x axis. Formula used: The volume of the solid is ∫ c d π ( f ( x ) 2 − g ( x ) 2 ) d x , where f ( x ) and g ( x ) are mentioned below. Calculation: Calculate the volume of the solid when the region R is revolving about the x axis. The curves are y = x 1 n and y = x n . Let f ( x ) = x 1 n and g ( x ) = x n . Let l = f ( x ) 2 − g ( x ) 2 . To find the volume of the solid, first find the value of l with f ( x ) = x 1 n and g ( x ) = x n as follows, l = ( x 1 n ) 2 − ( x n ) 2 = x 2 n − x 2 n To find the limit of integration, it is enough to get the point of intersection of the curves f ( x ) = 2 x ( 2 − x ) and g ( x ) = 0 . 2 x ( 2 − x ) = 0 2 x = 0 , 2 − x = 0 x = 0 , x = 2 Substitute the value of l = x 2 n − x 2 n in the above mentioned volume of the solid formula and take x = 0 as lower limit and x = 2 as upper limit b. To determine To evaluate: The limiting value of lim n → ∞ V ( n ) .

Calculus, Single Variable: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780134766850

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Question

Chapter 6.3, Problem 74E

To determine

To find: The volume of the solid in terms of n when the region R is revolving about the x axis.

To determine

To evaluate: The limiting value of limn→∞V(n).

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Chapter 6.3, Problem 73E

Chapter 6.4, Problem 1QC

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Calculus, Single Variable: Early Transcendentals (3rd Edition)

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The volume of the solid in terms of n when the region R is revolving about the x axis.

Solution Summary: The author calculates the volume of the solid in terms of n when the region R is revolving about the x axis.