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Volumes on infinite intervals Find the volume of the
Chapter 7, Problem 21E(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 \(f(x)=x^{-2}\) and the x-axis on the interval \([1, \infty)\) is revolved about the x-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 \(f(x)=x^{-2}\) and the x-axis on the interval \([1, \infty)\) is revolved about the x-axis.
ANSWER:Problem 21E
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−2 and the x-axis on the interval [1, ∞) is revolved about the x-axis.
Answer ;
Step 1;
In this problem we need to find the volume of the solid founded by rotating around
in the region
In order to find the volume, we will be using the following condition.
If f is a function such that for all
in the interval
, then the volume of the solid generated by revolving, around the x axis, the region bounded by the graph of
, the x axis (y = 0) and the vertical lines
and
is given by the integral
Volume