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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.7 - Problem 62e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.7 - Problem 62e

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

ISBN: 9780321570567 2

## Solution for problem 62E Chapter 7.7

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: = = = -

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