I Tried University of Texas Austin Integration Bee 2025 Finals

Added: 2026-05-12

[00:00:00]Wasabi, you guys. Let's continue on for the grand finals for University of Texas Integration B 2025.

[00:00:10]Looking at this already, I am terrified.

[00:00:13]Um God, I can already see some of the integrals that I cannot do at all. But Let's just uh Let's just go, shall we? If I don't know what to do, I just kind of you know, don't overcomplicate. Just do what I know.

[00:00:33]Um I was thinking about using Queen's rule, but Queen's rule is not going to help me.

[00:00:38]To not overcomplicate, we could do cosine 2x and then minus co- So, pretty much we have cosine on top. I'm going to do 1 + 1 - 1.

[00:00:50]So, I'll get cosine 2x.

[00:00:54]1 + cosine Something like that. I don't know if this would even make it any better. Cuz it's going to give me sin squared.

[00:01:03]Right? But, then this is cosine of 2x.

[00:01:06]Like, what do I even I mean, if you got if there's nothing you can do This This is just At this point, this just This is just bashing.

[00:01:16]So if we got to bash, we got to bash. I think I did that correctly. Okay, I hope I did that correctly.

[00:01:27]Oh, boy.

[00:01:29]Zero cotangent of zero is also zero, right?

[00:01:33]Wait, something's not right. Um yeah, something's not right. This diverges.

[00:01:39]Um something diverged.

[00:01:43]That's uh Okay, we're going to have to retreat. Uh Oh, my god. Yeah, I know. Queen's rule does not make any better. Why would you do this?

[00:01:57]This is so nasty.

[00:01:59]What the hell are you guys giving?

[00:02:02]What?

[00:02:04]Like is there even a trick to this? Or is this just pure bashing? Cosine squared over sine squared. Oh, maybe this is where I messed up. I messed up here. Maybe that's what it was.

[00:02:15]And then two cosine squared. Okay. Maybe that's what it was. I probably messed up here. I thought it was like one over sine squared, but it's cosine squared over sine squared.

[00:02:24]Okay.

[00:02:25]Now this is where I don't Maybe that's where I kind of drew.

[00:02:30]Okay. Now it makes sense. Wait, no, no.

[00:02:33]Even still then this same thing.

[00:02:36]Oh, no. But then I get this and this.

[00:02:39]Okay. Now that makes that they will cancel each other out. So, for cotangent and cosecant we get uh what? Cosine of X minus one.

[00:02:51]This?

[00:02:52]And this is going to equal to like what? Um zero?

[00:02:59]I think it's equal to zero. Wait, so is this equal to pi minus three then?

[00:03:05]That's way too clean.

[00:03:07]>> [snorts] >> That looks way too clean. Hold on. Ain't no way.

[00:03:13]Damn. Pi minus three. So, there was nothing at all. It was just speed bashing.

[00:03:21]Oh my god.

[00:03:22]I just had a bash.

[00:03:25]The holy hell.

[00:03:28]Y'all are wild. God.

[00:03:30]I just had a bash it.

[00:03:34]Woo. God. That was That was a difficult speed bashing integral.

[00:03:38]Okay. Yeah, I would There was no way I would be able to do that in five minutes. I'd I will I will panic way too much trying to find a shortcut.

[00:03:47]Okay. This you guys, I'm going to be real.

[00:03:50]I'm not very comfortable with multiple integrals. Like, I don't do I don't do multivariable calculus.

[00:03:58]I don't do calc three stuff. This is um This is This is a lot. But, like, I don't know the calc three techniques for this. I'm most likely not going to be able to do this.

[00:04:09]Like, what's the intention? I want to know the intention for this.

[00:04:13]But, yeah, I don't It's You definitely cannot do polar coordinates.

[00:04:21]I don't think you could do that. That only works if it's like x² + y².

[00:04:26]Right?

[00:04:27]I don't think you can do polar coordinates on this.

[00:04:31]It wouldn't be It It wouldn't be practical.

[00:04:33]Let me If I If I were to do polar coordinates, would it actually work? Am I even doing this right?

[00:04:41]I don't know if I'm doing polar coordinates correctly. I don't know.

[00:04:45]I'm just going off based off brain. Um But, yeah, this is like a constant.

[00:04:51]Right?

[00:04:52]So, s r Uh if I think about this in the Laplace way, it's just one over It's this, right? Mm, even then, I can't even do that.

[00:05:04]I genuinely don't want to do Weierstrass, but I might have to pull a Weierstrass on this. Ew, I don't want to do this.

[00:05:12]No, take me back to the other integral.

[00:05:16]Take me back to the other integral. Is it really zero?

[00:05:21]I refuse to believe this to be zero.

[00:05:24]There's no way in hell that's zero. Mm.

[00:05:27]So, I'm I'm doing this I did my double integral incorrectly then.

[00:05:31]I don't know. I don't do I don't do calc three stuff.

[00:05:34]Okay, I'm not even going to attempt this. This is disgusting.

[00:05:39]Come on.

[00:05:40]Let It's Queen's rule.

[00:05:43]Not even Queen's rule, actually. If you do Queen's rule, it's not going to make any better cuz then you do like you can do ln of tangent squared and you can just add it because zero the integral of zero pi over two of ln of tangent squared dx is equal to zero. So, you can just kind of bring that out and like multiply it. So, you'll get like ln of one plus five tangent squared plus ln of tangent squared plus five.

[00:06:12]That is disgusting.

[00:06:15]Oh god.

[00:06:18]No. No.

[00:06:21]No.

[00:06:22]Yeah, that's some that is I think this is like I think this is Feynman technique. Yeah, I I don't want to do that. I'm good. I'm going to pass.

[00:06:34]That's Feynman.

[00:06:36]You guys can go ahead and bash it yourself.

[00:06:40]I'm not in the mood for that. Okay, this looks interesting.

[00:06:45]I genuinely want to try this. What is the purpose of this?

[00:06:50]Or maybe I should have done this in the first place, but Oh, wait a minute. Oh, this is actually kind of sick. Wait, let you equal x over two.

[00:07:00]Okay, so this is this is actually kind of sick.

[00:07:05]Uh this is cosine minus sine and this is cosine squared minus sine squared for two x, right? So, du this is Oh, I take it back. I don't like this integral anymore.

[00:07:19]Um >> [laughter] >> I'm just so lazy. I've I'm sorry. I'm just I'm very lazy.

[00:07:29]So, now this is this is just secant. I plug in pi over four zero zero. Let's just zero minus ln of uh zero negative pi over four, that's like negative pi over four is here. So, you got to be careful. That's still root two, but then this is going to be minus one.

[00:07:52]Think I got this right.

[00:07:55]I hope so.

[00:07:57]I genuine I I will cry if I if I get this wrong. I It's a little iffy. You know what? I'm checking it right now. It's Uh it's a little iffy. It's a little iffy.

[00:08:10]Um plus, right? Yeah, from zero to pi over two. It is not a negative answer. I got negative ln of square Oh, actually, you know what?

[00:08:19]That might be Okay. No, I was right.

[00:08:22]Yeah, I forgot like this is the same thing as one over a square root of two plus one, and that's like that's positive in terms of logarithms.

[00:08:32]Okay.

[00:08:34]Well, then, I got it right.

[00:08:36]Holy Moses.

[00:08:38]>> [laughter] >> Woo! Okay.

[00:08:40]These finals are brutal. These These are very brutal finals integrals.

[00:08:46]There's There would be no way in the hell I would be able to do this in five minutes.

[00:08:53]They're very bashy, right? That's e to the x.

[00:08:58]Just right off the bat.

[00:08:59]One minus e to the Let me simplify that, actually. So, let's that's going to be e to the 4x.

[00:09:07]Uh notice I I noticed something right off the bat.

[00:09:11]Right, that this cancels out.

[00:09:15]And then whatever the heck this is. Oh, this is the same thing as one minus e to the 2x. Ah.

[00:09:24]Some good old problem shock, eh?

[00:09:28]So, this is just what what? One Oh, wait. Huh?

[00:09:33]Wait.

[00:09:36]Oh, no.

[00:09:39]Oh no.

[00:09:42]He did not.

[00:09:45]Oh come on. Don't do this to me. Oh actually, you know what? Let you equal e to the x. Sadly, this is indefinite, but Do you know what this looks like? What does this look like to you?

[00:09:58]This is something you would what?

[00:10:00]Let you equal Oh actually no, let let you equal sine theta. No, I'm You can you can still I was going to let you equal cosine theta, but No, actually that's This is actually perfect.

[00:10:13]This is cosine of 2 theta d theta and this is equal to This is the easiest.

[00:10:22]This is easier than quarterfinals. Oh my god. This integral is easier than most quarterfinal integrals.

[00:10:28]But nice problem shock. Very nice Or actually, it makes sense why they put this last. It could be like This was probably ordered last as like a like a tiebreaker, you know? Then then that that's actually perfect. This is actually perfect. A good nice problem shock.

[00:10:46]So, okay.

[00:10:48]In that case, this is sine theta cosine theta. Right? So, you get you this U is equal to e to the x square root of 1 - e to the 2x + c.

[00:11:05]If I am incorrect, uh please let me know. I will I will cry if I get this wrong. I will genuinely cry if I got this wrong. But wow, that wasn't not as bad as I thought. Um holy Moses.

[00:11:19]But yeah, that's it.

[00:11:21]That's all the finals. That's all the integrals for University of Texas.

[00:11:27]Unfortunately, I do not have the qualifiers. I don't know if they had one, but uh yeah, this was this was all I've found and I've gotten.

[00:11:36]So, yeah, um quite bashy. Half of these are bashy.

[00:11:43]Uh half of them are evil, and then half of them are nice.

[00:11:48]Um yeah. What the hell, man? Match one is so unfair. They get the easiest the easiest stuff.

[00:11:57]SMH My goodness. Same for match four, too.

[00:12:03]Uh but yeah, very fun.

[00:12:07]>> [laughter] >> Very very fun. Very nice.

[00:12:10]All right. Well, that's all the integrals for this integration bee, so uh I hope you guys enjoy that. Thank you guys so much for watching, and I'll see you guys in the next video. See you.