This chapter usually isn't too bad for most students as long as we're working in dx. Things get sketchier when we get to dy, though, and that's where you'll really need to practice to get good at these rather than just figuring, "Oh well, there won't be more than one dy problem on the test anyways." That's because even if the dy problems don't hurt you too bad on this test, these area problems are just a warm-up for the main act to follow: volume problems. And you'll need awesome dy skills for those, so don't gloss over dy problems now. You'll thank me.
Finding Area Using dx
When it comes to dx vs dy, students I've worked with ALWAYS prefer dx. It's just what everyone has been using for functions since they were introduced in Algebra 2. So we'll start with area problems involving dx (and thus functions of x) because it's the easiest place to start from.
Finding Area Using dy
This video starts with problems that are "obvious" dy problems -- meaning it's pretty straightforward that you need to use dy -- but then it moves into problems which are tougher to figure out whether to use dx or dy. By the end of this video, you'll be able to relax and let the problem tell you whether it wants to be dx or dy.
How To Decide Between dx & dy
In this video we pick up where we left off in the previous video, including working a problem in both dx and dy to see the difference. I also discuss how these problems relate to the revolved solids coming up in the next chapter, which are the most difficult topic in all of calculus for most students!
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...)