Explanation Given: The region bounded by the graphs of y = sin x 2 , y = cos x 2 , x = 0 and x = π 2 Formula used: We will use the Shell Method Calculation: We are given with the region bounded by the curves y = sin x 2 , y = cos x 2 , x = 0 and x = π 2 . First consider the graph of sin x and cos x , then it can be seen that sin x 2 and cos x 2 are even function. Now, find the intersection point of sin x 2 and cos x 2 . For this, sin x 2 = cos x 2 x 2 = π 4 x = π 2 Negative value of x is not taken because required region lies in the first quadrant. Hence, the sin x 2 and cos x 2 intersects at the point, ( π 2 , 2 2 ) . We get the required region is given by, Now, the bounded region is revolved around the y -axis then the solid obtained is, Now, Useshell method, the required volume is V = 2 π ∫ a b p ( x ) h ( x ) d x Where, p ( x ) radius of the cylinder is h ( x ) is height of the cylinder

10th Edition

ISBN: 9781285057095

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 8.1, Problem 88E

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The volume of the solid generated by revolving the region about the y-axis

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Chapter 8.1, Problem 87E

Chapter 8.1, Problem 89E

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Chapter 8 Solutions

Calculus

Ch. 8.1 - Choosing an Antiderivative In Exercises 3 and 4,...Ch. 8.1 - Choosing an Antiderivative In Exercises 3 and 4,...Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Choosing a Formula In Exercises 514, select the...Ch. 8.1 - Prob. 6E Ch. 8.1 - Choosing a Formula In Exercises 514, select the...Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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The volume of the solid generated by revolving the region about the y-axis

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Chapter 8 Solutions

To calculate:

The volume of the solid generated by revolving the region about the y-axis