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Solution: Volumes on infinite intervals Find the volume of
Chapter 7, Problem 24E(choose chapter or problem)
Volumes on infinite intervals Find the volume of the described solid of revolution or state that it does not exist.
The region bounded by \(f(x)=(x+1)^{-3}\) and the x-axis on the interval \([0, \infty)\) is revolved about the y-axis.
Questions & Answers
QUESTION:
Volumes on infinite intervals Find the volume of the described solid of revolution or state that it does not exist.
The region bounded by \(f(x)=(x+1)^{-3}\) and the x-axis on the interval \([0, \infty)\) is revolved about the y-axis.
ANSWER:Problem 24E
Volumes on infinite intervals Find the volume of the described solid of revolution or state that it does not exist.
The region bounded by and the x-axis on the interval [0, ∞) is revolved about the y-axis.
Solution
Step 1
In this problem we have to find the volume of the described solid of revolution or state that it does not exist.
We shall find the volume by using the following method,
“ If R is the region under the curve y = f(x) on the interval [a , b] , then the volume of the solid obtained by revolving R about the y-axis is ”