Split (1)

train · 116k rows

role stringclasses 2 values	content stringlengths 0 2.1k	session_id int64 10 21.7k	sequence_id int64 0 2.38k	annotations listlengths 0 8
volunteer	Um, all right. So, example 12. Now we have um	15,082	824	[]
volunteer	an improper fraction	15,082	825	[]
student	yes	15,082	826	[]
student	i solve it?	15,082	827	[]
volunteer	Yes, you solve it.	15,082	828	[]
volunteer	I feel like that's the best way to do um	15,082	829	[]
volunteer	the example problems because we actually have a solution and have it all written out. I think it's best that you kind of practice it on your own.	15,082	830	[]
volunteer	And then we can compare	15,082	831	[]
volunteer	the methodology	15,082	832	[]
student	okay, on it	15,082	833	[]
volunteer	Don't forget I have the table on the board.	15,082	834	[]
volunteer	So if you want to minimize the, if you want to minimize my screen to look at it.	15,082	835	[]
student	yes, i m looking at it	15,082	836	[]
volunteer	Oh	15,082	837	[]
student	done	15,082	838	[]
volunteer	All right, let's confirm.	15,082	839	[]
volunteer	Did you get	15,082	840	[]
volunteer	X minus 5 log.	15,082	841	[]
volunteer	X minus 2 + 10 logx minus 3 natural long, of course.	15,082	842	[]
student	oh no, i didn't	15,082	843	[]
student	i didn't change in proper frac	15,082	844	[]
volunteer	Oh, you just try to do	15,082	845	[]
volunteer	straight	15,082	846	[]
volunteer	X^2 + 1, try to integrate that straight.	15,082	847	[]
volunteer	What did you use as	15,082	848	[]
volunteer	your substitution	15,082	849	[]
volunteer	or your parameter	15,082	850	[]
volunteer	So that's what I was curious about	15,082	851	[]
student	i directly did like last question. i did it wrong way	15,082	852	[]
volunteer	Hm	15,082	853	[]
volunteer	Uh, you tried to find A and B immediately.	15,082	854	[]
volunteer	which you would have to do.	15,082	855	[]
volunteer	A + B + C. We had to have a a C term	15,082	856	[]
volunteer	cause you'd have	15,082	857	[]
volunteer	you have 3 equations, right? You got	15,082	858	[]
volunteer	an X^2 term, an X term and a 1 term, which doesn't really work out. And this is um	15,082	859	[]
volunteer	well, when we started this morning, this is what, what I	15,082	860	[]
volunteer	I was doing problems from the exercises. And there was one of them that had	15,082	861	[]
volunteer	um an improper fraction like this, and I was getting stuck the same way you are.	15,082	862	[]
volunteer	It wasn't until that we were reading the	15,082	863	[]
volunteer	the theory that I realized why it has to be an improper fraction to use this method.	15,082	864	[]
volunteer	And that we can't really	15,082	865	[]
volunteer	figure out straight, like it gets more complicated, we try to just keep using substitution method to solve these kinds of	15,082	866	[]
volunteer	uh improper functions.	15,082	867	[]
volunteer	Anyway, um,	15,082	868	[]
volunteer	I mean, you can do it the other way, but I'd recommend using	15,082	869	[]
volunteer	the methodology they give cause that's what we're here to practice.	15,082	870	[]
student	we can't use substitution here, bcuz how?	15,082	871	[]
volunteer	You could also use your method too to practice that. But right now they're just kind of they didn't want you to practice using this methodology.	15,082	872	[]
volunteer	because how we can't use substitution? Well, here's a question if we use substitution	15,082	873	[]
volunteer	what would we use	15,082	874	[]
volunteer	right? Because the numerator can't be	15,082	875	[]
volunteer	um	15,082	876	[]
volunteer	reduced any further	15,082	877	[]
volunteer	The denominator can be reduced to two expressions	15,082	878	[]
volunteer	and say you set T is equal to	15,082	879	[]
volunteer	one of the expressions	15,082	880	[]
volunteer	and you rewrote the numerator, you would still have an improper fraction.	15,082	881	[]
volunteer	or say you	15,082	882	[]
student	yeah, i reduced in two expression	15,082	883	[]
volunteer	converted um	15,082	884	[]
volunteer	say you converted this expression and instead of using tea, you decide to use a trig function.	15,082	885	[]
volunteer	and then you'd have to	15,082	886	[]
volunteer	try solving that way and I'd still be complicated.	15,082	887	[]
volunteer	Um, because you'd have, say, say you said that um	15,082	888	[]
volunteer	cosine theta is equal to X minus 2.	15,082	889	[]
volunteer	right	15,082	890	[]
volunteer	And then the denominator, you would have cosine, cosine theta, times, cosine plus one, right? So you'd end up with like co-signed squared plus cosine in the denominator.	15,082	891	[]
volunteer	But in the numerator, you have to rewrite it.	15,082	892	[]
volunteer	and it would still get complicated, right? You'd have like cosine plus something, cosine squared plus something, and	15,082	893	[]
student	it will be very complicatded, bcuz now we have polynomal andtrig	15,082	894	[]
volunteer	denominator cosines, cosine square plus cosine squared, and then you try to use the trigger identities and it's just too complicated.	15,082	895	[]
volunteer	Yeah.	15,082	896	[]
volunteer	Right. So those, cause that's just using the two methodologies that they've shown so far, right? Which would be substitution and trig identities.	15,082	897	[]
volunteer	Um	15,082	898	[]
volunteer	Now for the, the method they're giving here, well, I mean, I guess the other um methodology they give is just an antiderivation where you just look for	15,082	899	[]
volunteer	um	15,082	900	[]
volunteer	things that you know	15,082	901	[]
volunteer	are the derivatives of something	15,082	902	[]
volunteer	Um, but that isn't as straightforward here either.	15,082	903	[]
volunteer	So, um, and if we would go back, remember?	15,082	904	[]
volunteer	uh right here.	15,082	905	[]
volunteer	If P over Q is improper, right? And they define	15,082	906	[]
volunteer	proper fractions	15,082	907	[]
volunteer	such that the degree of P is less than the degree of Q.	15,082	908	[]
volunteer	right?	15,082	909	[]
volunteer	Then you have to do long division.	15,082	910	[]
volunteer	I know you try to do this problem without doing long division.	15,082	911	[]
volunteer	And that's why I, um	15,082	912	[]
volunteer	I don't know if you heard me when we were going through this, but I was kind of	15,082	913	[]
volunteer	trying to emphasize, you know, how do they define what a proper and improper is.	15,082	914	[]
volunteer	and, you know	15,082	915	[]
volunteer	the long division process.	15,082	916	[]
student	yeah, I heard you. but i didn't took notice of it in question i forgot	15,082	917	[]
volunteer	Yeah, and that's one of those things that like, you don't realize is important until you start doing problems and you're like, oh, OK, I guess I do need to know why they phrase it this way or why we're using this methodology or in what conditions we use it in.	15,082	918	[]
student	yes right	15,082	919	[]
volunteer	Yeah, so don't, don't, don't be upset. That's the same trap that I fell into.	15,082	920	[]
volunteer	And I was	15,082	921	[]
volunteer	forced	15,082	922	[]
volunteer	out of	15,082	923	[]

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