Hey, I managed to remember this week! Woo! Maybe I'll actually succeed at making this regular again. Anyways, that test that I was talking about last week was taken, and we began delving further into integration, so I've got a fair bit to talk about today.
Okay, so I'll be completely honest with you, I don't exactly remember how the test went. What I can recall, however, is that I was able to finish relatively quickly (what a shocker) and that I felt pretty confident with it. Looking back on it and comparing it to my last post, I think I let the quiz corrupt my thoughts on the chapter as a whole, and I anticipated a much more difficult test. While I don't doubt that the little bit I studied helped (I'll be honest, I didn't study nearly as much as I implied I would; I probably spent ten minutes max on it before becoming bored and going off and doing something else) I think that I'd have done fine without studying at all. Granted, I haven't gotten my score back yet, so this could all just be an illusion my mind is creating to make myself feel better about what happened, but I think I actually did fairly well. As I'm typing this I'm starting to remember more, and I think the multiple choice went by real fast without any trouble. The free response section was a lot of math (and, for the first bit, without a calculator. Multiplying to get common denominators isn't the most fun thing in the world, let me tell you, and neither is having to add seven-ish stupid numbers together to get a massive fraction that came out to something like 1191/1680.) but after looking over my answers, they all came out to be at least possible. My biggest fear was winding up with a number that didn't make sense, but each answer appeared to make sense given the relative shape and total possible area, and using extremely general shapes (basically just rectangles that loosely fit the figure) helped me to set an upper boundary that shouldn't be exceeded in the answer. For example, there was a small curve that fit within a 1 by 2 rectangle; logic dictated that the area couldn't be at or over 2, and the answer I wound up with was less than that, so I settled with it. Whether or not that actually helped me at all remains to be seen, but regardless, that's how I operated. This paragraph is getting a bit lengthy though, so I'll cut off my rambling here and move on to the next bit.
The rest of the week was spent on section 6.2, which consisted of a lot of integration. I found it fairly easy, so I'm not going to talk much about it. What I will say, though, is that I've lost my ability to integrate in my head. I used to be able to integrate some of the more complex things without u substitution or any of that stuff, but I've, for whatever reason, become unable to do that. I don't know why, the problems (at least early on) weren't any more difficult than before, but I'm still struggling. It's not a bad thing, necessarily, as I'm able to integrate using the u substitution, but it's a bit annoying that I can't do it as well anymore. I've been doing better at it with trig functions though, for whatever reason, so I guess that's nice. Anyways, aside from my own petty things, nothing too bad. 6.1 today was kinda dumb though, I really don't like these slope fields. They're ugly and just look like a random mess to me, and while I'm certainly not an artistic person by any stretch, I have to say that they bother me. I understand (to some degree) how they can be useful, but I feel like the imperfect graph they can create is more of a hindrance than a help, and having to make a bunch of graphs to account for the literally infinite number of possible constants just seems tedious. I feel like one could just fill in an entire graph (in certain situations, of course; not every graph will be able to cover every possible point with an infinite number of vertical shifts) and call it good because, technically, it shows every possible graph. I feel like I'd lose points on that though, and while I like to be dumb about things on occasion, I'd rather not let it affect my grade.
So yeah, that's that for this week. Long rant on the test that I didn't remember and then later remembered and a rant on slope fields, that's more than I usually do. I should get a medal or something. Anyways, next update is (hopefully) Friday, and I'll see you then.