You Laugh, You Integrate... [ feat.
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- Опубликовано: 2 окт 2024
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"Everything is convergent if you're brave enough"
I'm definitely taking this attitude to my next calc exam
No don't
I dare you to use the Riemann series theorem (or whatever it’s called) and just rearrange terms to show every divergent series converges to 69. ;)
ikr
@@sigmundfreud4472 Nice. And username definitely checks out.
Your prof be like: "Everything is a failed exam if you're brave enough"
"-420 is approximately zero"
"yeah for small values of 420"
lmfao
No I missed the moment this comment reached 420 likes
@@Smitology it still is at 420 for large values of 420
Andrew’s integration skills make me feel smarter
If there's only one thing I know it's that \int lnx = 1/x
@@AndrewDotsonvideos xDDD
Andrew replied ^_^
Are we not talking about flammy just being a dumbo with d^2/(d^2+1)?
@@thephysicistcuber175 they were both clowns the entire video
Clever memes:
Flammable Math:
"Your sister could be dead":
Flammable Math: LMAO DEAD SISTER
:D
I never knew I needed competitive meme integral solving, but I need it
:D
"Anything is convergent is you're brave enough"
I try to live my life by that marvelous phrase
Spoken like a true physicist
There is nothing better than trying to solve integrals while a german guy laughs at you, it is definitely as good as it gets...
Please keep this series alive haven't laughed this much in a while. Really keep this series going ahead.
:D
@@PapaFlammy69 can you integrate the gamma function please
Andrew: *breathes*
Jens: "Haha you laughed!!!"
:D
12:07 "proof by knowing what the answer is" lmao 😂😂😂
7th grade me wished i could have used it
I'm so happy that I'm not only who forgets if int ln x = 1/x or int 1/x =ln x
Dude, the last one's trivial. e = pi, so the integaral evaluates to zero.
they are making that joke in the video sir
When you realise that he could have just drawn some triangles to find the area under f(x) = x
If this is the level of humor you acquire when doing maths then I'm never stopping doing it.
:D
It does come with some problems...like trying to convince anyone other than other mathematicians that you are sane.
Andrew’s integration skills are making me wish that I stayed in my mathematical career.
You can always use the mail.
It’s never too late to switch.
"Reading the rest of the meme is left as an exercise for the viewer" killed me
"Whalecum to another video" 😂
AGGHHHHHH
🐋 💦
"good morning fellow mathematicians, welcbaktnuda veedio"
accurate
19:22 You could have done +1 - 1 in the numerator and split the fraction
It will become Integral of [1 - 1/(d²+1)]
So that will be d - (arc tan d) + D
Andrew laughs while internally dying at 9:28 after being reminded of massive American college debt oof.
I hope for him that it's not that bad
For the last one i used the "area method" since x is a simple function and the shape of area is just a trapezium
= (f(π) + f(e))(π - e) / 2
= (π + e)(π - e)/2
= (π² - e²)/2
= π²/2 - e²/2
Ikr idk why he didn’t graph it Lmaoo
Yeah. The area method is really simple. But it might be too easy.
Jens: Good morning fellow mathematicians
Me (A mechanical engineering major): *Nervous sweating*
"Everything converges if you wait long enough" ~ Andrew Dotson.
Favorite quote of the video: "Proof by knowing the answer".
xd
Me, an Aerospace engineer student: "Mhh, I see nothing wrong here."
Definitely doing this with my friend as a preparation for our upcoming calculus exam! 😂❤️great inspiration
Dude that is a brilliant study strategy for many classes, now I just need friends
Nobody:
Not even Americans:
Jens: "Hee"
Yet it is CORRECT !!! I'm Greek so ... I know how to pronounce it
Shut the fuck up about "nobody" already
INCOMING ANGRY EUROPEANS
I put the first integral into wolfram alpha and it told me “no result found in terms of standard mathematical functions”... holy hell
New result didn’t drop
OMG Papa Jens, I think you made a mistake! Are you sure about interchanging the limit and the integral at 8:20? The evaluated integral does not depend on ∂ anymore, so the answer would be something with Si(x) because you could ignore the limit.
The way you are doing it, you should include the d∂ in the limit, but then the integral would not make any sense.
Whatever he did there was definitely not correct lol. Since the integral from 42 to 111 is already a constant which does not depend on the variable, the limit would just be the constant. So the actual value of this limit would then be approximately -0.0054 according to wolfram alpha.
The notation was ambiguous to start with, so one could argue that the ∂ appearing in the integrand is not the one from the integral, but the one from the limit. XD
It's like taking the limit as x-> 0 or 6.
@@adamjennifer6437 Fucking bot.
For small values of 420 it is approximately 0...
Seems legit
Andrew is proof you don't need calculus to do physics
I mean he was probably rusty on integration or something, cuz you can go a long time without encountering serious integration while doing physics.
But when you are solving real problems, you better know integration.
@@takeuchi5760 you can study maths and go a long time with out integration
@@leoman5481 Yes except that the connection of branches in mathematics is just a mess, like for some reason the zeta function which is defined in the complex numbers gives information about the distribution of primes, which is dealt with in number theory. You just cannot say that you will never encounter integrals if you are a professional in other branches of mathematics.
Integrate x dx. Everyone: it's x^2/2...
Him: let's substitute bs here and use e^some more bs.
28:43
"Eins... Epstein's theory of heat capacity"
Wtf!?!?!
daily reminder that heat capacity didn't kill itself
Andrew killed Epstein
This is absolutely amazing! as someone who enjoys integrating but doesn't love it, it was an amazing way of practicing, I paused and solved each integral with you guys! Although it began as procrastination I ended up practicing!!! And my exam is in 3 weeks!! Thanks!
Engineers: Where's the table??
Honestly true. I thought. These techniques and what the heck is a sec^2. That's gotta be in a table. Otherwise I am lost. I call it proof by someone elses work
@@HormersdorfLP LMFAO
Dude, a great collaboration! Awesome to see you guys at it again!
For the d^2/d^2+1, you could add 1 and subtract 1 in the numerator, so (d^2+1-1), then split into 1-(1/d^2+1) which integrates into d-arctan(d)+C
NOTICE ME PAPA FLAMMY
Just sayin', but you could've just rewritten it like this instead;
(d²+1)/(d²+1) - 1/(1+d²)
and avoided all that monstrosity lmao.
"Everything converges if you wait long enough." Spoken like a true physicist Andrew.
Please don’t learn how to integrate from these guys XD
Just not from this video
Yeah they do some very stupid shit lol
Flammable maths interchanging the limit and the integral sign when the resulting integral is independent of the limit to end up with a complete nonsense result...
You could've let the memes away and just solve stupid integrals lol
Me: solves one simple integral in high school
Also me: „You lough, you integrate“
The first integral is Coxeter’s integral. In Nahin’s Inside Interesting Integrals it was THE single, longest evaluation in the book.
Is one a nerd if one finds this genuinely entertaining?
nope
no
Yes. Source: am a nerd and finds this genuinely entertaining
nah
No. Source: I find this genuinely entertaining but I'm dumb as a brick.
"python can't do things like 420^71"
ah, you appear to have forgot about one of python's coolest features, unbounded sized ints!
Literally laughed my ass off for nearly the entire video 🤣
:D
Does anybody else watch his videos even tho you have no idea what he is talking about?
you could've just had him come upstairs instead of overlaying the videos
No he needs to stay in the basement
Evere heard of covid-19?
honestly, I was laughing more about how you calculated the integrals in Dotson manner, than about the memes :D
And I thought I was the only physics student who fucked up integral and differential of log!
My shame has been vanquished. Thank you Andrew and thank you Flammy!
:D
31:00 since pi = e = 3, then the result is 0 since we integrating from 3 to 3
Whenever I have doubt about my integrations skills watching Flammy's "hard integration" videos, I watch this.
Then, I feel instantly better about my skills lmao
Mother 1/Earthbound Begginingsmusic. Hell Yeah!
Absolutely awesome!
I think u should extend your Wortschatz of variable names by integrating symbols from other areas of maths like group, category and set theory. Then you will be unstoppable.
8:24 you can't interchange the limit and the integral, instead you have to use the sine integral function Si(x)=int 0..x sin(x)/x. lim x->0 [int 42..111 sin(x)/x dx]=lim x->0 Si(111)-Si(42)=Si(111)-Si(42)≈-0.00543373
Love the Forest Haven music in the background.
24:40 integaral
Came for the memes, stayed for the math
22:05 take (d² + 1 = t) then differentiate it. (d.d(d) = dt/2). Now just replace the values in integral and you've an ans. [ln(√(d²+1))].
The solution to integral 3 was super cool!
8:35 You can't interchange the limit. As written, you are asking for the limit of a constant number, so for example you could replace that limit with one approaching 72 and your answer shouldn't change. But by interchanging, you are taking the integral of a constant, and this constant does depend on the value the limit is approaching, but that wouldn't be the case if you were free to interchange them through the integral.
You are playing too loose with dummy variables. The definition of the definite integral requires that its dummy variable be free to vary throughout its region of integration. When pulled inside, the limit that uses the same dummy variable places an additional restriction on the dummy variable that breaks the original definition of the definite integral.
My thoughts exactly, the area function limit might differ for the general case
Yeah, that integral didn't make too sense honestly. Letting a variable approach a constant but also integrating with respect to the same variable? Doesn't really make sense honestly
Joke's on you, papa flammy. Python can calculate arbitrary large numbers, including 420^71.
f u c c
19:44 that is the easiest integral of the whole video just +1 and -1 in the numerator and then separate the denominator, thus then you have to Integrate dd and -1/d^2+1 dd so the answer is d - tan^-1(d).
+C oops
Hey FM, this is one of the best formats you have presented. You can def. milk this cow.
But it's soooooooooooooo much editing XD
Integral at 20:00 is really easy. Just add 0=+1-1 to the numerator, and then it's trivial
this stuff reminds me of my time doing personal tutoring, amazing :D
Hello there
Hey :D
General Kenobi
@@backyardcreeper this is the right answer
General Kenobi
I have been trained in your Jedi arts by Count Dooku...
Proceeds to do the most unDooku thing possible....
You can see Andrew's agony in his face...that pain...
19:50 use long division. d^2/d^2+1=1-1/(1+d^2) which is trivial
In the dd one, you could have added and subtracted 1 on the numerator so you have 1-1/(d^2+1) in the integrand getting d-arctan(d) easier.. But I loved your struggle with the d's so I'm not even mad
The d^2/(d^2+1) would have been easier if you divided the polinome getting 1-1/(d^2+1)
“Take a deep breath such that you don’t laugh”
I've been using the same wallet since grade 6 lol
Number 9: just write d^2 +1 -1 kid flammy 19:20
Was gonna say... simplifies to d-(1/d^2+1) which are both standard integrals...
u still need tan substitution to integrate 1/(d^2+1)
@@tupoiu Not if you just say it is tan^-1 and leave the proof as an exercise for the reader.
As I was saying, standard integral
For the last integral, I would of used the graph to approach it visually and calculate the trapezoid using (upper base+lower base)*height/2 area formula
What about that arccos(f(t)) integral? How to solve that? It's in 4:31...
The anti-antiderivative of ln(x) is 1/x
You uploaded this faster, nice.
thE inTegral oF lOg(x) iZ 1/X 11:18
Please make more of these
The pikmin music got me
At 23:00, why didn’t he just add one to the numerator and subtract 1/(1+d^2), then you get 1 - 1/(d^2+1), which is d - arctan(d).
Great vid tho!
This is a useful and instructive video contemporary! :)
Now we know who is superior at integharals, that is, but the differential boii still is in the basement :D
For number 3 you could have used integration by parts with u=x,dv=dx.
What an astonishing video, I should be studying, but YLYI is much better. Thank you for the entertainment.
this is the best video on the internet
Oh my god I need more
Worse than you laugh you loose😂
Jens and Andrew: *struggle when using common letters as variables*
Greeks: First time?
Well watching this makes feel less dumb
Don't worry about some mistakes, it's just like Grandmasters blunders in Chess.
Hello Papa Flammy is the answer to the first question zero. I do it by substitution and integration by parts.
Papa not seeing, that f(chi) = chi is just a straight line, so integrating over any intervall [a;b] will be 1/2 * (a+b)(a-b) [using the area of a trapezium]
A great play along at home game!
@ 8:24 You can't interchange the limit and the integral in this case because the limit is respect the variable you are also integrating. If you work it out then you find that the answer is approximately -0.00543 (\int_42^111 sin(x)/x dx).
i was like number 3333 oooh
20:58 When a physicist beats a mathematician...
4:23 Engineer move ; )
Favorite cover photo enhance my joy
Of laughter joy !