Let R be the region bounded by the graphs of , x = 1, and the x-axis. Draw the solid obtained by rotating R around
The region R looks like this:
For each problem we need to label the axis of rotation, draw a mirror image of R on the other side of the axis of rotation, then make curvy lines so things appear 3-D. Curvy lines are the technically correct term. If you don't like curvy, you can also use words like winding, snaky or even serpentine. Our goal is to eventually use these images to help us build our integrals.
For each of these, we will draw R, the axis of rotation, and then the mirror image of R across the axis of rotation. Then we will make curvy lines to make volumes out of the two areas. We will see that same region R can be used to make very different solids of rotation just by changing the axis of rotation.