Explanation 1) Concept: i. If x is the radius of the typical shell, then the circumference = 2 π x and the height is y . ii. By the shell method, the volume of the solid by rotating the region under the curve y = f ( x ) about x - a x i s from a to b is V = ∫ a b 2 π x f ( x ) d x where 0 ≤ a < b 2) Given: y = tan ⁡ x , y = 0 , x = π 4 ; a b o u t x = π 2 3) Calculation: As the region is bounded by y = tan ⁡ x , y = 0 , x = π 4 ; a b o u t x = π 2 , draw the region using the given curves. The graph shows the region. A typical cylindrical shell is formed by the rotation about the line x = π 2 It has the radius = π 2 - x Therefore, the circumference is 2 π π 2 - x and the height is tan ⁡ x To determine b) To evaluate: The integral ofthe volume of the solid

8th Edition

ISBN: 9781285740621

Author: James Stewart

Publisher: Cengage Learning

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Chapter 5.3, Problem 22E

To determine

a)

To find:

The integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis.

To determine

b)

To evaluate:

The integral ofthe volume of the solid

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Chapter 5.3, Problem 21E

Chapter 5.3, Problem 23E

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a) To find: The integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis.

Solution Summary: The author explains the integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis.