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 line y = -1
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.
The real solid looks like this, with a cylinder missing from the middle.
Now that we've got a feeling for what some of these solids look like, let's start finding their volumes.