Explanation Let y = f : [ a , b ] → R be continuous and f ( x ) ≥ 0 . Consider the curve C given by the graph of the function f . Let S be the surface generated by revolving this curve about the x -axis. We will define the surface area of S in terms of an integral expression. Let us find the area of the surface generated by revolving the curve y = 1 2 ( x 2 + 1 ) ; 0 ≤ x ≤ 1 about the x -axis between the interval [a, b]. Here the function y is increasing hence it is one-one and onto. Hence, the volume of object formed after rotation is given by V = ∫ a b 2 π f ( x ) 1 + { f ′ ( x ) } 2 d x = ∫ a b 2 π { 1 2 ( x 2 + 1 ) } 1 + x 2 d x = ∫ a b π ( x 2 + 1 ) 1 + x 2 d x Also, we can write x in terms of as x = 2 y − 1 ...

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 6.4, Problem 61E

To determine

The function of which the curve when rotated about the x-axis, the region R under the graph of given function for given interval equals the volume obtained by rotating the same region R about the y-axis.

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Chapter 6.4, Problem 60E

Chapter 6.4, Problem 62E

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Chapter 6 Solutions

CALCULUS (CLOTH)

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - 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The function of which the curve when rotated about the x -axis, the region R under the graph of given function for given interval equals the volume obtained by rotating the same region R about the y -axis.

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The function of which the curve when rotated about the x-axis, the region R under the graph of given function for given interval equals the volume obtained by rotating the same region R about the y-axis.

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Chapter 6 Solutions