Find the volume of the solid generated by revolving the region bounded by and around the x-axis.
First, we need to find the intersection points of the two graphs. These are easy to find with these particular points. The intersections come at . Since is greater than between 0 and 1, and because we are revolving this region about the x-axis, our outer function is . So, we will find the volume of the solid of revolution using and subtract from this the volume of the solid of revolution using . That is,