INTEGRATING ONE WEIRD SHARPY BOI ( integral max{1,y} from 0 to ln(x) )

[@stumbling]

You speak English very fluently. If it weren't for your accent I would never guess it is your second language. I assume your first language is algebra.

[@46pi26]

To anyone saying it's "overcomplicated": shut up and just listen to his accent. That's the main reason any of us are here, and the longer we hear him talk, the better. But he's still a damn good mathematician.

[@46pi26]

Georg Cantor nah the best part is when he exists

[@46pi26]

Georg Cantor but the "boi" is still gold

[@RadicalSolver]

46 and pi The integral is easy to calculate without all this stuff about zero, so how's that make him a mathematician at all?

[@angelmendez-rivera351]

RadicalSolver It’s educative to teach it the hard way. This integral, while not having any real singularities, is still a great illustrative example of what should be done in cases with singularities. Furthermore, when it comes to ironic, unexpected humor, it’s a masterpiece.

[@megauser8512]

LOL!

[@Babidi123]

one line solution. integrate 1 dy from 0 to 1 and integrate y dy from 1 to ln x.

[@warrickdawes7900]

I agree this is the first thing I thought of too. However, if we did that then we would miss out on a fascinating bunch of integrals of absolute values, some epsilon limits, and a continuous solution (I think) that produces a stepwise answer.

[@eneaaiello3394]

Esattamente

[@eneaaiello3394]

nitish goel maybe 1 from 0 to 1 and y-1 from 1 to ln(x)

[@subramanianrs5618]

I too done this in that way

[@SKO_PL]

The absolute value isn't defined at zero... right. Wait what?!

[@hedgechasing]

I don’t know why this had to be so complicated... either ln(x) is less than one or its greater than one if it’s less than one then max(1,y) when y ranges from 0 to ln(x) is just gonna be one for the whole interval so the integral would just be ln(x) and if it’s greater than one, you can break the integral into two pieces one from zero to one where the max function will give you one so the total area will be 1 and then an integral from 1 to ln(x) and the max will then just give y so the total will be 1 + ln^2(x)/2 - 1/2 or just (1+ln^2(x))/2

[@nullplan01]

Case by case analysis: 1. If 0 < x < e, then ln x < 1, so y is always less than 1. So in this case the integrand is 1 for the entire range, thus the integral is ln x. 2. If x >= e, then the integral can be split into an interval from 0 to 1, and an interval from 1 to ln x. First integrand is 1, second integrand is y. Apply high school knowledge to arrive at 1/2 + 1/2 ln² x. Write both down as the answer for their respective case and you're done. The integral is undefined for x

[@bohittle6589]

"FUCKING AMAZING MY BOIS" - math dude , 2018

[@Photo650D]

The future of language used in scientific papers!

[@thomashaas4381]

This seems overly complicated and some reasonings you did were not accurate at all. The absolute value function is continous but not differentiable at x=0 (which does not matter for the integral at all). Also the cases ln(x) 1 can be directly used to split the integral in two integrals from 0 to 1 and 1 to ln(x): Suppose ln(x) > 1 then the integral from 0 to ln(x) over max{1, y}dy can be split into "Integral from 0 to 1 over max{1,y}dy" and "Integral from 1 to ln(x) over max{1,y}dy". In the first case max{1,y} = 1 and in the second case max{1,y} = y. Using this, you directly get the "integral from 0 to 1 over 1dy" which is 1 and the "integral from 1 to ln(x) over ydy) which is (ln(x)^2 - 1)/2. Adding these directly yields the result.

[@GreenMeansGOF]

I know, right. I solved it like that as well. No need for absolute value. Then he warned us that the video was going to be long and then I thought, I must have done something wrong.

[@Charlestopio]

DerKleineTomy then I bet you could do it better, congrats

[@angelmendez-rivera351]

Yes, the integral was solved in an unnecessarily complicated way, but I’m perfectly fine with it. Let him do whatever he wants. Besides, it actually is very educational to see an example of what one should do for an integral if one encounters a singularity, and I consider his way of doing it to be a check of reality using an integral which one can verify easily via simpler methods. It is almost like setting preparation. And the sheer weirdness of how he solved it is also entertaining. Honestly, you people should cut him some slack. It’s Papa Flammy.

[@NachoSchips]

Am besten hat mir gefallen, dass du frei und auch deutlich gesprochen hast. Auch dein Plakat war schön farbenfroh und man kann alles gut erkennen

[@saitaro]

The impression of Vsauce was so good I brang together my whole family to watch that again. Thank you for that, Flam.

[@sandmann6851]

18:09 same Spiel 😂😂😂

[@tylershepard4269]

I don’t believe there is a singularity in |x| at the point x=0, however, there is one in the first derivative. Since we are integrating, we can simply split it into two cases and recalling that |x| is defined as -x, x=0, it’s an easy integral. But still a fabulous video!

[@gui1542]

Hey mate, great video. For these people complaining about taking a longer path or making it over complicated to solve the integral, just relax and enjoy the ride.

[@TuningFreak23]

You are making maths attractive again for kids who like dank maymays. You could explain some things a little bit more in detail for the non-mathematicians out here. (engineering student here)

[@besio4881]

Handsome + genius ; you are The Chosen One

[@fountainovaphilosopher8112]

Don't forget his usage of le memes. Everyone loves le memes.

[@twwc960]

I can't believe this video got so many likes! As many others have observed, this is a very simple continuous function. The fact that it is not differentiable at one point is not an issue as far as integration is concerned: this is NOT an improper integral and there is no need for limits or epsilons to be introduced at all. When ln(x)1, just split the integral into two trivial pieces and add the results. It is a two line solution and this integral could be on a high school calculus exam. This very weird video by a very good mathematician, together with the fact that he's complaining about headaches has me somewhat concerned.

[@RaresLitescu09091998]

That's exactly what I thought!

[@akeelhowell8944]

twwc960 you have said it all...

[@Photo650D]

Hope your Kopfschmerzen - ääh headaches - get away soon. Don't stress youself too much with the content demand KZbin seems to have. I've had exams the last weeks, too. Not they are over the next semester starts… feel you

[@Michael134096]

There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy. (W. Shakespeare, Hamlet)

[@shanmugasundaram9688]

The second part can even be simple.The question is not about the continuity of the integrand function.It is about the definition of the absolute value of the function. You can straight away part the integral from 0 to 1 and from 1 to log x.The desired answer will be arrived.

[@piotrliach]

I don't know why, but watching these videos help me relax. also, I feel like I'm learning a bit. win-win.

[@jaim3m3s]

Keep up the good work, fam!

[@mighty8357]

wtf is this man???? That integral would scare the hell out of me in an exam. Heck, I would burn my question sheet and run out of the classroom 10 times out of 10

[@copperfield42]

Mighty XD it only look scary, but is really super easy...

[@sandmann6851]

Man konnte alles gut verstehen. Sehr gut gemacht.

[@mythicmansam1082]

Love the content! Excellent video :)

[@paraskhosla5640]

Could we not have taken simply two cases: Case 1: max{1,y}=y if y \ge 1 Case 2: max{1,y}=1 if y \lt 1

[@mighty8357]

3:50 you write ln(x)/2 instead of /4

[@echopotato]

I come to his channel for fun maths and humor like the one in 5:15

[@angelmendez-rivera351]

Also, I’m still waiting on my Antiderivative of sign(x) and sign(x)^2

[@paparapiropip87]

18:10 same Spiel 😂 that boi speakin Gerglish

[@Oleg_Ivanov]

Why didn't this integral take more easy: int(max(1,y) dy) from 0 to ln(x) = int(1 dy) from 0 to 1 + int(y dy) from 1 to ln(x) = y from 0 to 1 + y^2/2 from 1 to ln(x) = 1 + ln^2(x)/2 - 1/2 = ln^2(x)/2 + 1/2 ?

[@mark_tilltill6664]

Yes very good.

[@henselstep]

Why to use the easy method, if you can choose an overcomplicated method... Simply integrate the first integral from 0 to e and from e to ln(x) (if x>e) and all would be easy

[@BardaKWolfgangTheDrug]

May poor lovely boy is so hated here :< dont cry snowman

[@Legacies87]

Are you really a human or member of Avengers??very awesome question and video

[@MoodyG]

At 2:18 you say "x is in R", but it can actually only be in 0>>inf :D

[@saulgarduno7773]

3:44, shouldn't it be ln²(x) over 4?

[@sansamman4619]

ha,hmmmm... so I'm not the only one who gets headaches ;-; . eat these to get better, they help me out... -Apples. -Whole Grains. -Oats. -Bananas. you can also search online if you hate visits to the doctor like me xd i hope you do well in your exams :)

[@justwest]

4:30 - obviously it is continous!

[@noway2831]

Couldn't you have split the problem into two cases, one where ln(x) e \end{cases} \] Desmos graph: www.desmos.com/calculator/xqbgleo9mp

[@mipmip4575]

that thumbnail though XD

[@krisbrandenberger544]

@ 16:09 The signs of the last two terms should be reversed.

[@-aaa-aaa]

Out of curiosity, is there a general definition for the max of n inputs? i.e. max(a0, a1, a2, ... an)?

[@-aaa-aaa]

Yeah but that very quickly turns into an expression uglier than your mom.Maybe if the inputs were thought of as specific outputs to some polynomial? Maybe do a regression and find the maximum of that?

[@angelmendez-rivera351]

Conceptually, it makes no sense to talk about the maximum of several inputs unless each input is itself a function of a common input. Perhaps in set theory one could also use it by having every element of a set as an input and this would evaluate the maximum element of the set. Other than that, though, there is no way to make it conceptually even be coherent, let alone actually have a definition.

[@megacarlosloki]

Second part is just: waat?

[@FrancisZerbib]

Why simple if we can make it (very) complicated

[@lisafehlau1547]

Hana ♡ :)

[@RadicalSolver]

The videos are interesting and quite entertaining, but you have some mistakes and you might have some corresponding conceptual misunderstandings. For example, you pointed at the graph of a function that is a translation to the right by one unit of the absolute value function, and you said that it is not continuous because it is not differentiable at 1 (the "sharpy" point). That's incorrect. The absolute value function is continuous on its domain, the real line, and that property of continuity is preserved under translation. You're correct in saying that this function is not differentiable at the number 1, however. Now, the theory of integration goes not require differentiability of the integrand at all, so this is a red herring, ie, it is merely a distraction. I stopped the video to make this comment, so I'm not certain how you plan to use this lack of differentiability to help computer the integral at hand. I'll probably comment again when I've seen the rest.

[@guilhermeguimaraes1858]

When u say linearity what it means ? i dont get it, on Laplace... on a Linear Velocity distribuition... What does Linear means ?

[@copperfield42]

a linear operation means that: f(a+b) = f(a) + f(b)

[@guilhermeguimaraes1858]

Just that simple ? Now i get it ! I tried looking at google and some forums and all i saw was things involving Linear Algebra which i dont like very much... Anyway TY

[@benjaminbrat3922]

It is related because integration, like derivation, and most transform are linear operators. And to be a little bit more accurate, the operation/function/transformation/process f is linear iff f(a*x+b*y)=a*f(x)+b*f(y) with a and b constants (additivity and homogeneity of order 1).

[@FedericoYulita]

Easy integral solved in an overly complicated way... Why? I love your videos man but I don't understand why you chose to solve this in the most long and difficult way imaginable.

[@nicbajito]

The Kirtpole i'm ok with him, i like to know new ways for the same exercise.

[@mihaiciorobitca5287]

Bajito TM Probably that is a worming up gor other more complicated exercices,idk ?

[@jemcel0397]

Hmm? ln^2(x)/2 instead of ln^2(x)/4?

[@danieleferretti9117]

Can you integrate for me | Li[3/2, exp(i pi x)] |² from 0 to 1 ?

[@danieleferretti9117]

I'm pretty sure the answer is Zeta(3) but I'm looking for a suitable way that doesn't imply any series representation... but I wouldn't be surprised finding out there just isn't any one

[@rizkyagungshahputra215]

is it singular when the y=1?why?

[@cycklist]

Sign of u sounds the same as sine of u. Must pay attention.

[@MathLady42]

Wouldn't u * sgn(u) just equal |u|?

[@angelmendez-rivera351]

An Anarchist Yes

[@nacholopez7348]

Well that's the point isn't it?

[@oliverfrancescoriccetti1391]

?_? I can’t see this video, it doesn’t start. I can only see the preview pic and the loading circle. (I’m from Italy)

[@kibayuuto6634]

Alexander 3.14 yup from uk too

[@lisalisa9706]

What do you mean by "non zero set"? Did not quite get that

[@dirkovic2112]

I think it just means a set not including zero. So you could have f(x) = 1/x without having to worry about 1/0, because 0 is not included.

[@pauliunknown8118]

A for effort

[@willyou2199]

memes

[@pituitlechat3807]

Nice video even if i don't all understand... I think also that at 3:45 there is a mistake : ln²/2 in place off ln²/4?

[@Rundas69420]

If you accept Puzzles or Challenges from viewers, please check your youtube inbox.

[@yuval2be]

You said you want to "travel" the hald distance between a,b , so why isn't is just b-a? You said b>a, so why do you work with |a-b| if you already know it is b-a? Same for the 1-y..

[@natan9065]

Yuval Tuby He shouldn't have said b>a. In the integral y could be greater than or less than 1 therefore absolute value is required.

[@yuval2be]

I understand... Thanks!

[@kubrayilmaz128]

help mee:(((((( integral max (1,x^2) =???? please see me and helpppppp. i cant solve this questions .very harddd please

[@rockybond42]

3:44 Du bist ln(x)/2 geschrieben, es sollte ln(x)/4

[@nacholopez7348]

Du hast*

[@nacholopez7348]

Du hast mich*

[@nacholopez7348]

Du hast mich gefragt*

[@nacholopez7348]

UND ICH HAB NICHTS *GESAGT*

[@davidseed2939]

TRULY DREADFUL. 20 minutes of board work and the wrong answer. The graph of max (1,y) doesnt look like as drawn For y 1. It doesn't seem reasonable to assume x>e , ln (x)>1

[@BedrockBlocker]

lul

[@iustintaga]

Use sin instead of syn , please

[@angelmendez-rivera351]

You mean sgn(x) instead of sin(x)? But those are two different functions!

[@ekaingarmendia]

( * ) u ( * ) ----------------

[@copperfield42]

you solve it in a overly complicate way, so you let me no other option other than dislike the video... though I solve it with your same transformation of the max function, you do a bunch of unnecessary step like the syn function or the epsilon thing, and the absolute value can be remove before of integrating... and as DerKleineTomy said is even more easy like he said...

[@angelmendez-rivera351]

David Franco Let the man live his life. There is nothing wrong with over complicating the integral. Half of these KZbinrs do this quite often anyway, but usually it works out for the better. And it’s entertaining to see the weirdness of how this works even when overly complicated.

[@angelmendez-rivera351]

David Franco Also, for the record, it’s sign.

[@akeelhowell8944]

Sorry dude but as others have said, I had to dislike this one.