The formula for these problems is simple, it's usually the algebra that gets you. But since there's only a few ways to contrive these problems so that the algebra (and ensuing u-sub integral) actually work out okay, once you've seen a few of these problems, you've really seen them all. These are those problems.
Area of Revolved Surfaces
The word "revolved" tends to give calc students unpleasant flashbacks to washer and shell methods, but these surface area problems aren't nearly as bad. So follow the few tricks in this video, and avoid the common mistakes I almost make, and you'll be okay.
If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list (not that we recommend cramming, but when in Rome...)