Refer to the figure and find the volume v generated by rotating the given region about the specified line.
r3 about ab

Hence, volume is: cubic units.

Step-by-step explanation:

We will first express our our equation of the curve and the line bounded by the region in terms of the variable y.

i.e. the curve is re

and the line is given as:  

Since after rotating the given region about the line AB.

we see that for the following graph

the axis is located at x=1.

and the outer radius(R) is:

and the inner radius(r) is:  

Now, the area of the graph= area of the disc.

Area of graph=

Now the volume is given as:

On calculating we get:

Volume= cubic units.

the final function for the graph becomes x-2=-1. before graphing you solve the equation, where x=1. then graph accordingly.   ( on the x-axis, 1 on the line will possess a vertical line.)