Volumes of Revolution: Revolving about a vertical axis

[Beeorz]

Homework Statement

Find the volume of the solid obtained by rotating the region under the graph of y=1/x and y=1/x^2 about the vertical axis x=-1

Also given are points on the y-axis (0,2) and (0,5). I guessing these points are specific sections of the graphs where we find the volume.

Homework Equations

Volume of revolution = pi int_a^b ((R^2)-(r^2))dx

The Attempt at a Solution

For this problem I would think...
a=2
b=5
but I am uncertain as to how to find R and r. I know they correspond the outer and inner radii but how do I go about find them.

I attached a picture of what the problem looks like.

 

[HallsofIvy]

Homework Statement

Find the volume of the solid obtained by rotating the region under the graph of y=1/x and y=1/x^2 about the vertical axis x=-1

Not "under" the graphs, between them.

Since you drew a picture of the curves, also draw the line x= 1 and imagine a horizontal line from from x= 1 to those curves, for a given y.

Also given are points on the y-axis (0,2) and (0,5). I guessing these points are specific sections of the graphs where we find the volume.

Homework Equations

Volume of revolution = pi int_a^b ((R^2)-(r^2))dx

The Attempt at a Solution

For this problem I would think...
a=2
b=5
but I am uncertain as to how to find R and r. I know they correspond the outer and inner radii but how do I go about find them.

I attached a picture of what the problem looks like.

You are rotating the outer graph, y= 1/x², around the line x= 1. R is the distance between those two, for each y: 1- 1/x². r, the inner radius, is the distance from the curve y= 1/x to 1: 1- 1/x.