2023 MIT Integration Bee - Finals

[@justinhj1]

If we play this backwards it can be the differentiation contest

[@harryallen5392]

was not supposed to laugh this hard, thanks man

[@kshiteeshbijjula8000]

Nice one

[@yashchaturvedi864]

wow. this is genius! good one!

[@Mymellowsouvlaki]

Genius! Lol

[@Lakshyarajkalra]

Good one hahah!

[@mitchellsteindler]

Best part of this is that nobody at MIT could make a program where the dude just presses a button to both start the timer and show the problem.

[@sovietcitrus]

the integral on the screen is only for the audience, the competitors have individual cards that they look at

[@mitchellsteindler]

@@sovietcitrus yeah I learned that at the end...

[@mitchellsteindler]

@e doesn't make it okay...someone in the audience could have been communicating with a contestant through a wifi connected butt plug. Duh!

[@ian-hm6cx]

@@mitchellsteindler ahh yes, the hans neimann method

[@nathanhammond523]

Literally put together a google slides with timer in 5 minutes. There was even a chrome extension already made.

[@iowa_don]

I have a degree in physics, a degree in Mechanical Engineering and I’m older than dirt. But I have to say, the phrase “3, 2, 1 integrate” is one of the funniest things I have ever heard. It makes me laugh every time I think of it.

[@TONI__KROOS]

how old are you

[@iowa_don]

@@TONI__KROOS Older than dirt, past 70

[@maxgeorge1463]

How difficult is it to attain a degrees (minimum a masters) in physics? How has your experience in the field of physics been? I am considering a degree in physics on a path to medical physics.

[@MaskedChieff]

😂😂😂

[@shaleenparikh2750]

😅

[@abhikalpshekhar]

Imagine the commentary: Its a good trick by Joe who looks to convert like into trigonometric form , while John makes excellent use of complex numbers to simplify the terms , it seems as if Joe has the upper hand here , but john now elegantly applies feynman's trick and gets the answer, what a twist in the tale

[@Mr.Divorce]

Definitely performing the integration using complex analysis

[@april-rf3pq]

what a twist!

[@ASCENTxyz]

I would watch it

[@BilalAhmed-wo6fe]

😂😂

[@edwinjoy9]

The commentator would have to be at least as talented as the person who's solving haha

[@Crustyislooking]

its so interesting to see the difference in the way they work the problems

[@shoaibakram5973]

nothing like that ..... the problems they presented can be solved by b tech students india with no difficulties

[@leandre1523]

nope @@shoaibakram5973

[@ryanhi6199]

@@shoaibakram5973 NAH. I didn't see any indians in that room

[@zirtzi]

@@shoaibakram5973there might be Indians who can solve them, but to be it in 4 mins is insane.

[@indiancyberteam]

​@@shoaibakram5973you're wrong about that

[@tazukiswift1588]

Seeing that guy on the left do the partial fractions by just looking at it for 3 seconds then writing the answer has to be the most impressive thing I've ever seen

[@_Longwinded]

Watching him winning other tournaments on YT and you’ll be even more surprised. :)

[@FishSticker]

@@_Longwindedhis name?

[@oscarzhu3470]

@@FishSticker Luke robataille I think? edit: oh wait sorry that was the guy int he right

[@lordkorvo_2089]

@@FishSticker maxim li

[@Marco-sm9bu]

time stamp?

[@neonelectron5066]

probably the first time I saw an integral being solved in arabic

[@vickensemerdjian]

It's okay this is the first time I saw an integral being solved at all.

[@naders.]

U look so unfamiliar!😂

[@Indian_Polar_bear]

😂😂

[@yourfriendlyneighborhoodqu3859]

technically they all are because we use arabic numerals

[@themesera3527]

wait which one

[@ZygalStudios]

MIT almost seems like a parallel reality. A world where anti-differentiation is a sport and people film it on their phones is a world I desire to be a part of :)

[@lunam7249]

cal tech is better.....where the 7yo high school graduates go

[@happytravelling]

@@lunam7249 The mascot of MIT is the Beaver - the Engineer of the animal world!

[@lunam7249]

@@happytravelling GOOOOOOOO BEAVERS!! !!!!!

[@Elausis]

¡Ponte a estudiar!

[@bilkishchowdhury8318]

The parallel reality is in my cranium

[@vedantbhatnagarmathur4488]

I never thought I'd be watching an Integration competition but here we are

[@user-banny44nc]

Although I’m just a high school student, but I’m still trying to understand what are they doing. I found a quit intriguing part: The guy in the left he is using the blackboard as his eraser paper, writing down all the process and calculate. The guy in the right is different, he calculate the operation by mind and he use the blackboard as an extended-memory cache, to write down the process just for not forget and loss them, like a redstone repeater, which I found it was impressive for me.

[@mujtabaalam5907]

It's the most efficient, writing is slow compared to thinking. That's what you'd expect from a four-time IMO gold medalist

[@vedanth_2609]

if this is coming from what I assume is an IITian which means a JEE Advanced cleared candidate with less than 16k rank atleast, I cannot assume how smart or hardworking you have to be to reach Luke's level!@harsh_will_iit

[@sixmet]

Insane. I suck in math. watching these guys solving a super hard integral in less than 4min (even if they got a wrong answer) is ridiculous.

[@randomacc77777]

@@Snakesake2099lol. I did many Jee advanced problems but they’re never even CLOSE to MIT entrance exams or even these so called ‘avg high school’ questions.

[@frostackerman]

@@randomacc77777bruv the bees stung Chelsea. Good job there

[@whereswaldo1376]

@@Snakesake2099 Sure bro... Keep trying to be patriotic about your 3rd world country bud

[@randomacc77777]

@@Snakesake2099 u aren’t fooling anyone. I’m Indian and I used to live in india before and I’ve been through the system. You’re blatantly lying lmao

[@PRATEETSANTRA]

Yeah got into iit Bombay now in second year I can easily do this

[@souvikdas]

This sport should have commentators. If there's one sport that needs them!

[@zachsheffert5811]

There are commentators for the like 2012 one or something. Also on yt

[@jamescollier3]

"Does Dan have no clue? Is he bluffing and scrawling?"

[@paarasshemrudkar1025]

It would be irritating

[@Paul-fu2xv]

They'd have to have a degree in mathematics to comment 😅

[@psikoexe]

I think that would distract the participants... math is a game of critical thinking and focus. If its added separately they must make sure it gives various possible solutions and some intellectual input instead of some crazy clown shit. I liked it as it is tho.

[@tjpprojects7192]

Hah! This is too EZ! I can also solve this problem in 4 hours just like they did. I'm glad they sped up the video though.

[@IwasabletoDisappearafterlitsen]

😂

[@samarthshukla9869]

You guys can solve this?

[@IwasabletoDisappearafterlitsen]

@@samarthshukla9869 you even know how to draw that Snake thingy before Numbers and Alphabets?

[@samarthshukla9869]

@@IwasabletoDisappearafterlitsen heh nice one

[@rangerworld8446]

@@IwasabletoDisappearafterlitsen Integral lmao not that hard tbh

[@nimrod9]

I actually tried solving some of these and was able to solve a few (but none from the finals though, and none in the stipulated time period). Glad I've still got a bit of integration in me! :)

[@maxvangulik1988]

I thought i had #5 but the geometric sum thing might be from 0 to infinity so maybe a 1 was subtracted?

[@maxvangulik1988]

Wait that would give 4/3 how tf

[@maxvangulik1988]

I would like the fact-checkers to show their work.

[@w.i.l.dyoutube4166]

@@maxvangulik1988 The reason its not 4/3 is because each term has the floor function

[@maxvangulik1988]

@@w.i.l.dyoutube4166 at the time i didn’t realize that floor of (2^n)x where x is between 0 and 1 isn’t just 0

[@baseduck]

This seems like something I would have had a nightmare about during high school and woken up in a cold sweat. It's been over six years and I still have flashbacks to AP calculus.

[@simunator]

christ, ab and bc are child's play compared to calc 3 and advanced calc.

[@isaacfitzgerald9348]

I have an A in calculus 2 with my final a week from today and this completely humbled me

[@_Longwinded]

Luke I’ve been following him from his primary grades and always saying he’s the next big thing in maths One of the finest brain always winning now in college wow Congratulations! Inspiration his YT channel is also worth visiting

[@HSA-]

@@shashwatdubey5416 will not be revealed since that's part of creating the suspense around him. You will have to search YT and see if it really exists or not

[@_Longwinded]

@lukerobitaille3404 with ~2k followers

[@JoshT13]

ayo thats creepy af

[@YoutubeDeletedMyLastNick]

You made that sound weird unless you know him in person

[@deuce2293]

@@JoshT13 It's not that creepy because he's literally everywhere. You see him somewhere in basically every video related to olympiad/competitive maths.

[@hardboiledegg2681]

managed to solve some of these but none in the time limit they had, these people are incredible

[@markkennedy9767]

Well so far I'm drawing with them after the second integral.

[@u.v.s.5583]

I could hold up with both of them until the last one, where Luke slightly beat me, but losing 0:1 after 5 rounds is fine in such super elite level.

[@rameneater5620]

@@u.v.s.5583 be sooooooo fr

[@yugiohsc]

I’m so happy the integration bee is still going on. Playing along is very relaxing

[@englishlife5838]

Omg luuuuke was in the math olympics competition too. He is a grown college kid now. So proud

[@pegenwaukegan4792]

Blessed be God’s Holy Name forever!

[@preetamchatterjee1723]

4 times gold medalist!

[@mathematicalmuscleman]

Integral Calculus is a Power House of Methods and Techniques.

[@r.f2173]

like your mom

[@SloaneCarrillo-c6y]

These guys are truly integrated lords!!!. Gives new meaning to the phrase "Show your working".

[@BengalAmbientGuild]

Gives new meaning to the phrase "Show your working"🙂

[@railx2005]

Them: shows work in arabic

[@m.s.dawood6985]

26:20 luke has the answer correct *agressive handshake*

[@jin_cotl]

They were nervous 😂

[@stevenveloz2995]

Begs commentary / analysis during / after the competition. Remarks from the competitors would be great, also.

[@r.f2173]

they're both obviously pretty neurotic, I think the last thing they want is a one-on-one interview lol

[@genovayork2468]

​@@r.f2173 They aren't "obviously neurotic" lmao, from where do you get these?

[@identitystolen1467]

Congrats Luke, both very smart people.

[@jimmelton]

@John They have to have some sort of great intelligence to get this far into the integration bee, don't see why there was any need for this comment lmao.

[@chikenwingsteve]

@John Understanding that these guys are judged to be smart enough to compete during an intergration bee is indeed very short sighted, but yet you were too blind to see that...

[@mkay7359]

@John luke is a 4 time gold medalist in international math olympiad...

[@laKennyr]

@John don't think u have any idea how hard it is to even be an audience in that place

[@attran720f]

​@@laKennyr Everything is hard for those who not understand it

[@Renthlei_Jr]

I watched Luke win another competition last night(an old one, while he was in middle school or so) and I saw this again tonight. Pretty impressive

[@NoGames-x1p]

27:42 the way how they both wiped their hands after this wet awkward handshake💀😭

[@michaelg9334]

It's really cathartic having finished undergrad and knowing I'll never have to actually solve calc problems like these again

[@acerniss]

It’s so interesting to see their contrasting methods and handwriting

[@kalebhawkinson9528]

26:23 top tier sportsmanlike handshake

[@nikosandrianopoulos4185]

The left guy was drawing very beautiful fences.

[@gabriel4970]

Damn 4 minutes is what i spend writing down the problem lmao, congrats Luke :)

[@epicm999]

2-D??? What're you doing here???

[@ArifSolvesIt]

to me too. I don't know how they do it. I could solve the first one in 20 minutes :-) :-) kzbin.info/www/bejne/rYCll5KDp7aJhNE

[@studentscouncil659]

26:25 that handshake was personal 😂

[@RicardoGandicaGG]

Damn, Tom scott here grinding those integrals is not what I expected here

[@GrandmaSkillz]

dang luke still out here winning math competitions

[@integralfreak1296]

Luke's integration methods are intriguing, he integrates in weird approaches compared to conventional ones like the guy in blue shirt did

[@capbanana3851]

Luke tends to find the patterns, shortcuts, symmetries etc in a problem whereas Maxim uses more standard methods and sort of brute forces it

[@nikhilsharma3999]

most of the time if you want to solve definite integral use king property because that always gets you somewhere

[@paull2937]

MIT integration bee 2023. Nice how it rhymes.

[@NavChetna0]

i got it ahh!

[@HariChera]

It will continue rhyming every ten years now

[@jebbush3130]

26:24 best handshake of all time lmao

[@johnchessant3012]

16:55 oops

[@carterneedscoffee6421]

It’s almost 2am. I have work tomorrow. I don’t know any math higher than algebra. Why am I watching this.

[@pruthavpatel9606]

Good to see Luke winning the bee, following since the mathcounts days

[@-.SkyArt.-]

Not only did Luke win this, he was also a multiple time winner of MATHCOUNTS internationals and many more competitions. He truly is very capable of many things.

[@nebula3415]

MATHCOUNTS is probably one of the least impressive of his allocates his a 4 time imo gold medal winner

[@Phymacss]

@@nebula3415he’s a genius

[@-.SkyArt.-]

@@nebula3415 woah really?

[@rutvikchaudhari869]

The answer of Q.4 should be 5 * 10^18 * ln(1001/999) ,which is equal to the answer written in decimal. Luke get almost right answer but he got ln(1003/1001) which is the only part wrong in the answer. The arbiter said there is no 5, but there is. We can't solve log on the board with time limit.

[@partevstepanyan5587]

Problem 1 I=int ((tan x)^1/3/(sinx+cosx)^2)dx from 0 to pi/2 I= int ((tan x)^1/3/(cosx(sinx/cosx+1)^2)dx= int ((tanx)^(1/3)dx/(cosx)^2(tanx+1)^2) u=tanx I=int(((u)1/3)/(u+1)^2)du from 0 to infinity u=t^3 du=3t^2dt I=int(t*3t^2/(t^3+1)^2)dt from 0 to infinity, integrate by parts I=-t/(t^3+1)+int dt/(t^3+1) from 0 to infinity, -t/(t^3+1)=0 if t=0 and t=infinity int dt/(t^3+1)=( 1/3)*int dt/(t+1)-(1/3)*int (t-2)/(t^2-t+1)dt=1/3*log(t+1)-(1/6)*log (t^2-t+1)+(1/2)*int dt/(t^2-t+1), 1/3*log (t+1)-(1/6)*log (t^2-t+1)=log ((t^2+2t+1)/(t^2-t+1)^(1/6)=0 if t=0 and t=infinity I=(1/2)*int dt/(t^2-t+1)dt=(1/2)*int dt/((t-1/2)^2+(√3/2)=(1/2)* (2/√3*arctan(2t/√3-1/√3) from 0 to infinity I=1/√3 (pi/2+pi/6) =4/6√3=2√3pi/9

[@mehrannazari8288]

😎 awesome

[@benjamimica1842]

most impresive thing is you did the work of writing it in a youtube comment tbh

[@triathlontimmy]

42?

[@r.f2173]

such a honky no one cares HAHAHAHAHHAHHHAHAHAHA

[@cinnamonshake45]

no one cares? i see only you here 🤔🤔

[@MathTutor1]

It is very interesting to see their excitement. Good job guys and Congrats Luke!

[@Mo-on4zl]

Love the enthusiasm in the handshake at the end!

[@tanaygupta1926]

I'm surprised by the fact no one in the video or even in the comment section realised that, in 21:16 , they both got the answers correct! coz if you simplify their answers, you'll get the same answer as that given by the MIT. It's a shame to judge the answers as wrong just because they were not written exactly same or it should not be 'a multiple of 5'. Integral answers often exist in many forms. They both should have gotten a point for that.

[@jiannanjiang8608]

There is a nontrivial floor operation at the end.

[@itsZybn]

The subtle "Fuuuu-" at 17:05 😂 my guy had one job

[@DH-oy6vy]

The handshake after the last problem 😄

[@Tots314]

Mfs talkin bout how they kept up with these students, but you already know the moment they walk up to that chalkboard they gonna be 10x slower than anyone in there

[@goob6433]

I watch this before my Calc homework just to know it could be way harder

[@omshiva5264]

helped me revise my integration chap for jee adv thanks mit.😄

[@aspirantjee2023s]

Bro kitne percentile aye first attempt me?

[@m.s.dawood6985]

@@aspirantjee2023s i got 98..

[@omshiva5264]

@@aspirantjee2023s 90 nitw me hu yaha se partial drop lera so bas cutoff clear kara for advanced.

[@aspirantjee2023s]

@@omshiva5264 all the best bro

[@aspirantjee2023s]

@@m.s.dawood6985 nice, I got 97.7

[@miaduque8014]

Somehow my YT algorithm brought me here. Im not good at maths but it was awesome to watch!

[@notacasual5593]

Tom Scott doing Integrals is something I didn't expect.

[@NavChetna0]

10:18 OH THE WHOLE THING IS SQUARED lmfao😂😂😂😂😂😂

[@АрсенийАйдаев]

Fun fact, ~20% of the commentators are just random indians trying to flex

[@rpsinghgaur5903]

Flexing for a reason

[@Flexyshores]

I don't know why, they don't try to feel mathematics. They just spam in comment section and consider themselves very intelligent and brilliant.

[@Maths_3.1415]

​@@Flexyshores Exactly

[@Snehin-qr2bl]

​@Maths_3.14because you americans aint solving calculus in highschool15

[@4fgaming925]

@@Snehin-qr2bl true, I just started 11th, finished cengage(iykyk) and these were too easy(jk not easy but doable)

[@Lol-qy1dy]

Honestly, problems are doable and is not super hard. However it's important you finish in time before other person and dont make blunder under time pressure

[@mlkgpta2869]

Someone who prepared for jee advanced must've solved these kind of problems from cengage or sameer bansal or vikas gupta type books

[@garvicatorthefirst8128]

10:20 'Oh, the whole thing was squared'

[@AirborneAnt]

Wow!!!! Great job Luke!!! and a valiant effort for Maxim as well!!!! Bravo guys!!!!👏👏👌👍👍

[@DIDIpsyche1]

I'm not MIT good yet but I'm getting there... hopefully! :)

[@DIDIpsyche1]

@John haha well alright. if you say so.. I'm just going to enjoy the sun at the beach.

[@RegisteredLate123]

​@@DIDIpsyche1 w mindset you gonna get there brother

[@DIDIpsyche1]

@xxdxddddffwfegfg haha I actually am doing ok with the open university mathematics. mit is was just a hype in high school. of course, I am very realistic as open university mathematics and physics bsc is good enough for me.

[@DIDIpsyche1]

@@RegisteredLate123 lol let me first finish my undergraduate. I meant not to get into MIT but being MIT level of smarts which comes with doing well enough in maths like in my current undergraduate mathematics and physics bsc degree at the open university uk.

[@DIDIpsyche1]

@John I think I'm over Ivy League in terms of for prestige reasons. I'm better used to the content of the course available at that particular university and I'm happy with open university course description. so I'm good with uni at the moment just thinking about ability variation between various universities. so I am disabled and recovering from a genetic disease and I think that I can some day have exceptional ability so that's what I'm aiming for. right now I have above average performance at second year mathematics and physics bsc.

[@salus5319]

Honestly this doesn't seem too tough to me, I mean I was tied with both of them up until that last question.

[@MarcusHCrawford]

Lol.

[@paulregener7016]

Sound like you should join or do something that matches your skill!

[@khattakjarir3399]

😂

[@genovayork2468]

​@@khattakjarir3399 They're not at all tough lmao, you just sck at math. I'm in high school and two are easy.

[@khattakjarir3399]

@@genovayork2468 ?? the original comment was a joke who even are you 😂😂

[@matthieupaty5032]

Being MIT grand integrator of 2023 is a massive flex I'd say

[@createvideo561]

The last one was rather difficult until you realise that it's a infinite series with base 3/2 and x just goes out

[@gautamghosh5303]

As a physics major student studying Schrödinger equations this doesn't help

[@wiredweird4953]

Funny thing is quizmaster can not intergrate 2 tasks of saying "integrate" and "clicking for next slide" in same time

[@hangshinguite]

10:19 that laugh after a guy said "whole thing is squared" 😂😂man the vibe of this class..

[@zenshing3293]

My respect for India grows every second

[@baotutubenbenxiong]

瞬间感觉自己好厉害。当年高等数学补考才能过的人，现在快40了十几年没看过数学书做过题，第一个简单定积分我比他们算的还快还是心算的。这还是麻省理工的。

[@Vlad_the_goat]

luke 是数学奥林匹克四次金牌获得者, 数学不只是计算更多的是思维

[@pranshuchittora5444]

Me who is still trying to centre a

[@user-lu6yg3vk9z]

First problem need to factor out a cos(x) Third problem you need to use the concept of odd/even function

[@alexgodeye3031]

The interesting thing would be to see how they solve them,which Is not shown

[@babahijacker4265]

As a 12 grader pakistani student ,i gave a try to 1st question as it looked very simple to me and i just realised that its not for me

[@ishaankumar4587]

Because it is simple and 12th grade level

[@crim2331]

Mfs in comments be like: "maaan that's so ez!! I do these in 30sec (i am still in kindergarten) 🤓☝️"

[@CloneReaper]

u have a anime pfp bro pipe down

[@shubhamprakhar6932]

In TENET this would be a differentiation contest

[@kimikokimi]

You two have my respect. 🎉

[@krackr6618]

Bring back the commentary.. he was awesome.. pay them if required

[@johnajuwon174]

These guys are truly integrated lords!!!

[@Horizon24129]

These type of competition should be in iits also Where they can encourage student skills in diff fields of science

[@Inndjkaawed2922]

I got the 3rd problem... but the rest of them were super hard. The last one was particularly tricky... I think we have to use the continuity of the function. Hoping someone can help me with the last solution.

[@yni3240]

The answer is 3

[@idrisShiningTimes]

I tried to do it via Reimann integration but it's just hard for me But I tried with Lesbesgue integration and it can be done easily with that

[@4fgaming925]

3rd was quite easy, but putting in values might take some time

[@mustafacanyoldas4562]

its hard to believe its given in school exams in turkey and also on the most biggest exam for entering university the time also is 2 minutes for every question

[@aniketbasak1637]

3,2,1... Integrate The best phrase I have ever heard❤

[@pranavaggarwal7965]

One problem took me like 1 hour 😢 they work really hard for this

[@Jechew]

Luke Robataille was an impressive 2 time winner for Mathcounts some years ago

[@okflippy]

luke is in every maths competition i swear

[@Torq123]

I think at least 2 additional minutes to be given for the participants to first visualise and plan for the solution strategy.

[@r.f2173]

no

[@LiterallyJustMal]

you underestimate these guys the scores would go 5-5

[@indistantdreams]

26:27 and 27:42 -- both time the dude reflexes and cleaned his hand after the handshake.😂😂

[@lqtor5950]

My reaction in chronological order: *First question revealed* Oh that’s not that bad *Plug in pi/2 to tangent* Oh shit, that’s undefined Oh shit this is an integral, I have to find the anti derivative Oh shit you can’t u substitute this Oh shit I’m fucking lost

[@Inndjkaawed2922]

been waiting for this!

[@ScottESchmidt]

Three years of Calculus and none of these look even remotely possible to me.

[@PrinceKumar-hh6yn]

That's a nice way of training young minds

[@honestabe_9207]

The very first integral looks simple but is so HARD! Simplifying it into a different form (for the denominator) is easy, but trying to integrate it with typical integration techniques is seemingly impossible so that evaluation became a guess... I heard of Luke Robitaille from being an insane mathlete (MATHCOUNTS & IMO); thus, if he couldn't fully solve - who could? Jk

[@hbowman108]

I got that one pretty quickly but I doubt I would have finished in four minutes. It follows pretty simply from doing the substitution u^3=tan x. It looked like he was overthinking it.

[@honestabe_9207]

@@hbowman108 yeah I was just joking, but I didn't see how clever the reduction would become: ∫ [0, (π/2] ((3u^3)/(1+u^3)^2)du

[@MiguelHD04]

@@hbowman108 Yep the integral actually reduces to integral from 0 to inf of (3u^3/((u+1)^2)(u^2-u+1))du and then you just do parcial fractions. However, we all must admit that shit is not finished in less than 4 minutes lol

[@hbowman108]

@@MiguelHD04 I reduced to 3/(1+x³) - 3/(1+x³)² and the second one obviously has a contour integral of zero. Then you just have the pole at exp(pi i/3).

[@matteomontanari2960]

With enough time i can understand what the guy on the left is doing. The guy on the right is using his own notation

[@aazeenhussainali786]

i the beginning i thought the luke was dumb because he was not even writing the integration sigh then i realised that he was doing the entire procedure in his mind💀🗿

[@Chriib]

These are some really hard problems. Almost impossible to manage by brute force without knowing some sneaky tricks.

[@vishalmishra3046]

*Problem 4 was easy* Substitute Y = x^10 thereby setting numerator to 1 and denominator to an easily factorizable quadratic of x^10 with roots 23 and 25 with limits of integration changing to 2^10=1024 to INFINITY. F(Y) = 1/20 x ln | (Y-25) / (Y-23) | so F(INFINITY) = ln 1 = 0 and -F(2^10=1024) = ln(1001/999) = 2 x (10^-3 + 10^-9/3 + 10^-15/5 + 10^-21/7 + ...) times 10^20/20 = 10^19/2 (2s cancel next). 10^(19-3) + 10^(19-9)/3 + 10^(19-15)/5 + [ 10^(19-21)/7 + ... (these terms < 1 and don't matter) ] = 10^16 + (1/3)x(10^10) + (10^4 / 5 = 2000). ANS = [10],[000,00]0,000,00[2,000] + [3][333][333][333] = [10],[000,003],[333,33[5],333] = *10,000,003,333,335,333*

[@ADDISONxz]

This isn’t the right answer

[@vishalmishra3046]

@@ADDISONxz It is. Check the video again.

[@preeyanshagarwalla6499]

@@vishalmishra3046 how did you simplify ln(1001/999) i couldnt get it

[@Pudgy973]

How would subbing y=x^10 set the numerator to 1 considering it was originally x^9

[@xianjunlim]

@@Pudgy973 y=x^10 dy=10x^9dx

[@silva8675]

Tenho 15 anos e sei resolver integrais, derivadas e limites. Brasil acima de tudo.