Let R be our favorite region.
Use the shell method to write an integral expression for the volume of the solid obtained by rotating R around the line
x = 2
When we rotate R around the line x = 2 we get the solid
The shell at position x has height . Its radius is the distance from the curve to the axis of rotation x = 2.
The radius is
2 – x.
The volume of the shell is
The shells go from x = 0 to x = 1. This means we need to integrate from 0 to 1 to get the volume of the solid, or