I nearly forgot to do this, I managed to remember at pretty much the last possible second. Apologies for a lack of continuity, I'll probably be typing this up as a stream of consciousness, I'm heading off to bed after this. Oh, who am I kidding, I always do this kind of thing, it probably won't be much different from any others. On with the post!
We've finally arrived at rotations of curves and finding the volumes of the solids produced, and I have to say, it's not as bad as I'd expected. I mean, I don't really understand why the equations work, and I still feel a little lost whenever I'm fumbling my way through a problem, but hey, I seem to have at least a basic grasp on the concept. At least, the sub complimented my grasp on it, so I guess that's a good thing. She's also a substitute teacher though, so I'm not sure how much her praise is really worth, but it's something. I have a feeling it was mostly because I explained my work pretty terribly, and I was pretty much forced to assume everyone knew what I was saying due to my sheer lack of eloquence earlier on, and I might have defeated the purpose of the lesson (I may or may not have done it differently than the book wanted, I honestly don't know) but whatever, if I can do well in class I should be able to do well on the quiz Monday. If we even have one Monday.
I'd say my biggest issue right now is determining when and when not to square the integrand. It's kinda complicated, and I can never figure out whether I'm to square everything at once, one piece at a time, leave a bit out, and whatnot. I've basically resorted to always squaring everything no matter what though, and it seems to have worked out for the most part, so that's cool. I mean, it won't be cool if it fails me, but if I've been going about this the right way the whole time, I feel like I've made a good guess. It helps that I can kind of figure out a vague volume based on crude cylinders, so that helps out a lot too. If I feel like an answer is way off, I can always alter my equation a bit until it seems more reasonable, but that's really my approach to everything math-related.
Anyways, that's about it. Wow, this post probably took me the least amount of time, I actually knew what I was going to say beforehand. Kinda nice, hopefully the future will bring more of these kinds of situations. Regardless, I'm going to get some sleep, this week has been exhausting in general. Next update, as always, will be on Friday.