Big brain from Karthik at the end. Not sure if this was intentional, but going into Problem 5 with a lead means you can put the same answer as the opponent and guarantee a win
Actually tried the first on my own before watching and solved in a few minutes, it isn’t nearly as bad as it seems. Started with tan = sin/cos as I saw that then I could do u = cosx and the sinxdx can come from numerator of tan frac perfectly canceling all trig in integral. Then we have -int(1/u * sqrt(2+sqrt(4+u))) the next thought is that the double radical is pretty ugly, especially since there’s a +2. Thus I did another sub of t=inside of outer radica, 2+sqrt(4+u). I knew this would probably introduce some annoying terms with the dt part of the sub, but figured by rewriting the sub for u in terms of t as u = t^2 - 4t, we get du = 2(t-2) dt which is just an extra linear term, easier to deal with than the nested rad. After the sub we get -int(1/u * sqrt(t) du) which when subbing rest of ts in gives -2int((sqrt(t)*(t-2)dt)/(t^2-4t)) factoring out a t on denominator and canceling the t with sqrt(t) on num gives -2int((t-2)dt)/((t-4)(sqrt(t)))) This is a rational function integral with sqrt(t) in denom, and if anyone has seen sqrt in denom of into before they know an easy way to get rid of it is another sub w= sqrt(t) or w^2 = t as derivative becomes 1/2sqrt(t) meaning the jacobian/sub term takes care of the square root in the denominator while just making all the other linear terms into squares/quads which can factor. This makes integral = -4int((w^2-2)/(w^2-4) dw) = -4int((w^2-4+2)/(w^2-4) dw) = -4int((w^2-4)/(w^2-4) dw) -4int((2)/(w^2-4) dw) = -4int(dw) -4int((2)/(w^2-4) dw) = -4(w+int(2/(w^2-4))) From here this second integral is pretty standard and can be solved using partials fractions by factoring the diff or squares to get the answer in the video (after of course going backwards through all subs from w back to x) or, an easier way to solve it, is to use the derivative of arctanh(a) = 1/(1-x^2) and thus int(2/(w^2-4)) = -arctanh(w/2) this is equivalent to the ln part in the final answer by the properties of inverse hyperbolic tangent and therefore also leads to a valid answer, but in my opinion, is a little more elegant than the logarithms through partial fractions.
@@AhmedNazir really? i screenshotted a picture of the integral from the video, posted it on deepseek and got this response: "is highly non-trivial and may not have a simple antiderivative. Advanced techniques or numerical methods would be required to evaluate it." with no anti-derivative. On second glance I the screenshot I provided must not have taken the floor function surrounding the '2' and 'sqrt(x)' into account. Once I got a clearer picture of the second problem and posted it on deepseek it solved the problem.
chatgpt couldn't even figure the first one out lol. it said it "is highly non-trivial and may not have a simple antiderivative. Advanced techniques or numerical methods would be required to evaluate it." also, I'm confused about the link in the description to the problems and the ones in the video. The first three problems in the video don't show up in the linked PDF. What's going on there? On second glance I the screenshot I provided must not have taken the floor function surrounding the '2' and 'sqrt(x)' into account. Once I got a clearer picture of the second problem and posted it on deepseek it solved the problem.
Usually grad students at MIT write the problems. I may be wrong but I believe some of the ones volunteering by giving the finalists the slips of paper are some of those students
@VARMOT123 Yes, these are bit tricky but good for my practice. And Actually I did along with the video time limit. 🙂 Talking about pressure that may become bit problem but I still did with that. So it counts, i guess.
As an European it's always interesting to see that in the American finals you see mostly Asians and Indians. I know it's legit and I have nothing against that. But at first you wouldn't expect it. At least not as an European.
Has nothing to do with being Indian. It’s just people bro, whoever is better at solving integrals. why are you guys so fucking weird in every comment section. If Indians were truly specifically that extraordinary at solving integrals why are Indian winners so rare in this contest? Stop bringing countries into this, it’s just an individual accomplishment
btw they both werenot from america and just remember the innvation tht america is doing wouldnoit be possible without outsiders so yea no way they would do this(i am just giving innovation as a example?
as someone always comments each year, if you play this video backwards it will be a differentiation competition
And yet that is wronger than the existence of liberal women who aren't bops
😭
why the hell do i find this comment funny😭
Christopher Nolan will name the movie "TEN-integra-ET', where protagonist saves world by Integrating in Red and simultaneously differentiating in Blue
😭 bro logically you're right too 😂
Now Waiting for new bprp vid to explain this lmao
Math 505 already explained all of them smh...
@@gdtargetvn2418thanks for the mention homie
@@gdtargetvn2418that too 5 days earlier than this video to come up. 😅
Big brain from Karthik at the end. Not sure if this was intentional, but going into Problem 5 with a lead means you can put the same answer as the opponent and guarantee a win
New banger just dropped
This series is so satisfying to watch
Watching the MIT Integration bee for a year now and its great to watch keep it up guys
Been consistently watching the past few years. Just learned how to solve an intergral last week. ;-;
Same 😊
been watching for 2 years, still don't know xd
Which stream do you guys choose?
@@thakrratul1109 wdym, like pcm for 11 th and 12 th?
me too
If you watch this video in reverse it becomes "2025 MIT Differentiation Bee - Round 1"
if you play this backwards it would be the '2025 MIT Differentiation Bee - Finals'
😂😂😂
Not really, those are definite integrals 🤓
Always great to watch 🙏
Actually tried the first on my own before watching and solved in a few minutes, it isn’t nearly as bad as it seems. Started with tan = sin/cos as I saw that then I could do u = cosx and the sinxdx can come from numerator of tan frac perfectly canceling all trig in integral. Then we have -int(1/u * sqrt(2+sqrt(4+u))) the next thought is that the double radical is pretty ugly, especially since there’s a +2. Thus I did another sub of t=inside of outer radica, 2+sqrt(4+u). I knew this would probably introduce some annoying terms with the dt part of the sub, but figured by rewriting the sub for u in terms of t as u = t^2 - 4t, we get du = 2(t-2) dt which is just an extra linear term, easier to deal with than the nested rad. After the sub we get -int(1/u * sqrt(t) du) which when subbing rest of ts in gives -2int((sqrt(t)*(t-2)dt)/(t^2-4t)) factoring out a t on denominator and canceling the t with sqrt(t) on num gives -2int((t-2)dt)/((t-4)(sqrt(t)))) This is a rational function integral with sqrt(t) in denom, and if anyone has seen sqrt in denom of into before they know an easy way to get rid of it is another sub w= sqrt(t) or w^2 = t as derivative becomes 1/2sqrt(t) meaning the jacobian/sub term takes care of the square root in the denominator while just making all the other linear terms into squares/quads which can factor. This makes integral = -4int((w^2-2)/(w^2-4) dw) = -4int((w^2-4+2)/(w^2-4) dw) = -4int((w^2-4)/(w^2-4) dw) -4int((2)/(w^2-4) dw) = -4int(dw) -4int((2)/(w^2-4) dw) = -4(w+int(2/(w^2-4)))
From here this second integral is pretty standard and can be solved using partials fractions by factoring the diff or squares to get the answer in the video (after of course going backwards through all subs from w back to x) or, an easier way to solve it, is to use the derivative of arctanh(a) = 1/(1-x^2) and thus int(2/(w^2-4)) = -arctanh(w/2) this is equivalent to the ln part in the final answer by the properties of inverse hyperbolic tangent and therefore also leads to a valid answer, but in my opinion, is a little more elegant than the logarithms through partial fractions.
wow bro why arent u at mit
For a real challenge how about a few Cleo integrals?
haha i agree
saw the golden ration here in one of the questions and thought of her lmao
No hope of solving them within 5 minutes then unfortunately haha
finally they solved the time and showing up of question issue. the question wpould ususally show up after 5 sec of itmer beign started
I solved 2 of them under an hour of out 5.
New banger just dropped!
the fact that the deepseek R1 can solve these with 100% accuracy is insane
True, I had given the 2nd problem to Deepseek and it does give the correct answer 😲
All of them?
@@KishblockproI tried the first one. Deepseek R1 solve with 100% accuracy. I am totally amazed.
@@AhmedNazir really? i screenshotted a picture of the integral from the video, posted it on deepseek and got this response: "is highly non-trivial and may not have a simple antiderivative. Advanced techniques or numerical methods would be required to evaluate it." with no anti-derivative.
On second glance I the screenshot I provided must not have taken the floor function surrounding the '2' and 'sqrt(x)' into account. Once I got a clearer picture of the second problem and posted it on deepseek it solved the problem.
@@Fernandez218you need to enable Deep Think feature.
Will this integration bee cause the integrals in the exams to be harder?
We want Kartik vs Luke
Wow! Karthik Vedula defeated Brian Liu, the former Grand Integrator. Absolutely insane! 🔥
Telugu kids dominating all the bees . Spelling bee,geo bee and now integration bee
this is gonna be fun
i am gonna give advance this year lets some that i integrate whatever they want me to do so
bro i hope i will race here in 3 years etc.
LEZGOO 2025 integration beee
X,X2+5=8
Oh look--a real college major! One of the few left.
I love this presenter. I can't unhear the "sree, to, wor, insuhgrays"
Could you please explain how to solve problem 2,3 and 4?, I have never seen those kinds of problems
Please bring back the commentary.
Who is this person who hosts this integration?? Will he be able to solve all integrals??
I completed two of them by myself. Although I didn't time , I still enjoyed it . Thank you for the five given mathematical challenges .
Grand Integrators here
Yearly tradition for us at this point
I actually know the two finalists from math competitions in middle/high school.
I kinda fell off ngl.
Need help solving the first one, tried subbing u = lnsecx so that du = tanxdx but it made it rather confusing. Will retry; any other ideas?
First problem was diabolical
vocês postam tudo rápido demais, eu mal terminei de ver as semifinais e já tinham postado as finais.
Leaving a comment before I watch!
The super bowl of college academics. Congratulations to the true all-americans.
Liu almost got the second one
And problem 4 was so sad
Nice 👍😊
I like it 🇨🇲🇨🇲🇨🇲
chatgpt couldn't even figure the first one out lol. it said it "is highly non-trivial and may not have a simple antiderivative. Advanced techniques or numerical methods would be required to evaluate it."
also, I'm confused about the link in the description to the problems and the ones in the video. The first three problems in the video don't show up in the linked PDF. What's going on there?
On second glance I the screenshot I provided must not have taken the floor function surrounding the '2' and 'sqrt(x)' into account. Once I got a clearer picture of the second problem and posted it on deepseek it solved the problem.
Forgot to update the link to the problems (was 2024), should be fixed now!
Why would chatgpt be able to solve it?
@two697 I meant to put deepseek. but chatgpt can do some basic integrals, too. deepseek does a better job.
integral calc website can obviously solve it, but doesn't use the easiest u-sub.
@two697 idk why? but it did. it gave me the same numerical answer as deepseek did.
nice
floor function shenanigans.
3 questions were not that difficult
that's fun
Just bring out DeepSeek.
Integrals in 2025 🤡
Integrals in 2010🗿
where did the question come from (sir made it or ??? )
Usually grad students at MIT write the problems. I may be wrong but I believe some of the ones volunteering by giving the finalists the slips of paper are some of those students
Nerds!!!!
❤
I would like to add my solutions:-
1>(4+cosx)->t² let then proceeding I took, √(t+2) is gamma, and got final answer
INTEGRATE
I got 3/5 easy 🙂 btw am 16😅
In 5 minutes under pressure?
@VARMOT123 Yes, these are bit tricky but good for my practice. And Actually I did along with the video time limit. 🙂
Talking about pressure that may become bit problem but I still did with that. So it counts, i guess.
Telugu kids dominating it eh . From spelling bee,geo bees,3m young scientists to akash bodda and karthik vedula here
🇮🇳🇮🇳 Karthik 🇮🇳🇮🇳
Congrats , make America Great again.
But he is American born
He is American citizen.
Telugu kid @@ashishkumarsharma2584
Damn
Low key I've always wanted to compete in the Virgin Bowl...I mean the Integration Bee.
As an European it's always interesting to see that in the American finals you see mostly Asians and Indians. I know it's legit and I have nothing against that. But at first you wouldn't expect it. At least not as an European.
American's are not as hard working
Not one American is surprised....there's usually an eastern European also
Also India is in Asia
India is absolutely insane when the subject is integrals, absolutely insane karthik !!
@@gabrieltlgne3198 Europeans invented integral we rule the world, india never did anything lol
@@hibudyBro did not pay attention in history😂😂
EUROPE knew no shit pre industrial era now go and sleep @@hibudy
Um I mean thats an individual achievement, so lets take it that way.
Has nothing to do with being Indian. It’s just people bro, whoever is better at solving integrals. why are you guys so fucking weird in every comment section. If Indians were truly specifically that extraordinary at solving integrals why are Indian winners so rare in this contest? Stop bringing countries into this, it’s just an individual accomplishment
that shit is too easy
India vs China and supervised by China but all Americans or documented Americans
Wat
type shi
Yoo
nerdge
I'm happy to announce that I am an Indian
Third. Haha
braindead integrals
FIRSTT
First
Only real Americans should be allowed to participate 😑
btw they both werenot from america and just remember the innvation tht america is doing wouldnoit be possible without outsiders so yea no way they would do this(i am just giving innovation as a example?
Why?
you scared
Oh you mean the Native Americans, right? right? 😆 "Real Americans"
get a life lil bro