So, I'm a bit late once again, just getting to this a half hour before it's due. Whatever though, so long as it's on time, it works, right? The lack of update last week was due to a competition, and at this point it's a bit late to do a proper one, so I'll just throw everything into here. It's basically the same, anyways.
So, it's official. I have no idea what I'm doing with finding the volumes of these rotated graphs. I've aced the quizzes, yes, but I still don't know what I'm doing. All I've done is plug in the numbers where they go, using a simple formula each time and attempting to remember the basic rules for each method, but they haven't stuck for whatever reason. I still don't know when to use the shell method and when to use disks/washers, and I think that's probably a problem. I mean, you get the same answer either way (I think) but I don't trust myself to do it correctly if I accidentally pick the more difficult of the two. I suppose I'll see how well I did at guessing which method was ideal on the test questions in two weeks, though; I either did fantastically well on the test or I completely bombed it. That seems to be a running theme these past couple weeks, and I don't really like it all that much.
Basically, to reiterate my above point, I do not feel confident on this subject in the slightest. I don't know if it's due to the wall I've hit, having come back victorious from my competition and being a senior whose year is drawing to a close, or if it's something else entirely, but I feel like nothing these last couple weeks has really stuck. I mean, I can remember that the shell method is 2pi times the antiderivative of the radius (usually just plain x or y) and the height (usually just the function itself, or the difference of two functions), but the washer method has already slipped my mind. I think it was pi times the antiderivative of the outer radius minus the inner radius, quantity squared, but I could very well be wrong there. I sure hope not, I used that on the test, but I still could be.
All in all, I can really only say that I hope the test went well and that there won't be many of these types of questions on the AP test. I assume I'll be more well versed in the topic by then, especially given my awareness of my lack of understanding, but I'd still feel more comfortable if the volume questions were replaced with, say, simple derivation. That I can do. Anyways, that's all for now, next update in two weeks.