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Solved: When is the volume finite Let R be the region

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 62E Chapter 7.7

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 62E

When is the volume finite? Let R be the region bounded by the graph of \(f(x)=x^{-p}\) and the x-axis for \(x \geq 1\).

a. Let S be the solid generated when R is revolved about the x-axis. For what values of p is the volume of S finite?

b. Let S be the solid generated when R is revolved about the y-axis. For what values of p is the volume of S finite?

Step-by-Step Solution:

Problem 62EWhen is the volume finite Let R be the region bounded by the graph of f(x)= and the x-axis for x 1.a. Let S be the solid generated when R is revolved about the x-axis. For what values of p is the volume of S finiteb. Let S be the solid generated when R is revolved about the y-axis. For what values of p is the volume of S finiteSolution Step 1:(a)The volume of S is given by the integral If -2p = -1 (i.e. p = ½) , then this integral becomes = log aAnd the volume is infinite, If p , we have: = = = -

Step 2 of 2

Chapter 7.7, Problem 62E is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Solved: When is the volume finite Let R be the region