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
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!
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.
@@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.
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
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).
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.
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
@ 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).
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
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
Jens, at 19:37 you literally can add and subtract 1 in the numerator, then club them to be integral of (d^2 +1/d^2+1)-(1/d^2+1) dd. So then the first fraction gives d and the second gives arctan d after substituting d as tan d. Or you can do it the physics way which is remember that integral of 1/(d^2+1) dd is arctan d
You and Andrew are hilarious 😂😂 I cracked up every time Andrew had to say “approximately” when he had to integrate with respect to approximately. You guys should definitely do another one at some point.
For the problem at 30:18, could you take the definition of the definite integral to be the area under the graph of a function, and as such equate that to the area of the triangle formed under the graph i.e. 1/2bh ?
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
Hello Papa Flammy ! I really love what you do on your channel ! This concept is soooooo cool ! If one day I want to reuse it, can I ? Keep doing the great work !
I enjoyed the video ! Isn't the one at 16:00 wrong because of the argument used but gives the right result ? For me, the denominator is nor even or odd function but the denominator - 1/2 is odd, so you can write the all thing it as even(x)*(odd(x)+1/2) so you just integrate the even part times 1/2 and it gives the same results. Cheers !
Papa for χdχ just integrate by parts! Setting up the equation gives you int( χdχ ) = χ² - int( χdχ ). Add the integral to both sides and divide by two: You get χ²/2 ! :D
On integral #9, we could just use a quick long division on that ugly expression x² / (x²+1), we can turn it into 1 - 1/(x²-1) which is easy to integrate, it would just be x - arctan(x) + C :)
![You Laugh, You Math... [ feat.@AndrewDotsonvideos ]](http://i.ytimg.com/vi/ZpBWdzS-I7g/mqdefault.jpg)
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
"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
I never knew I needed competitive meme integral solving, but I need it
:D
There is nothing better than trying to solve integrals while a german guy laughs at you, it is definitely as good as it gets...
"Anything is convergent is you're brave enough"
I try to live my life by that marvelous phrase
Spoken like a true physicist
Clever memes:
Flammable Math:
"Your sister could be dead":
Flammable Math: LMAO DEAD SISTER
:D
12:07 "proof by knowing what the answer is" lmao 😂😂😂
7th grade me wished i could have used it
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
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.
I'm so happy that I'm not only who forgets if int ln x = 1/x or int 1/x =ln x
Jens: Good morning fellow mathematicians
Me (A mechanical engineering major): *Nervous sweating*
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
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.
"Whalecum to another video" 😂
AGGHHHHHH
🐋 💦
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.
Favorite quote of the video: "Proof by knowing the answer".
xd
Me, an Aerospace engineer student: "Mhh, I see nothing wrong here."
Andrew: *breathes*
Jens: "Haha you laughed!!!"
:D
"Everything converges if you wait long enough" ~ Andrew Dotson.
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!
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.
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
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
"Everything converges if you wait long enough." Spoken like a true physicist Andrew.
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
"Reading the rest of the meme is left as an exercise for the viewer" killed me
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.
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
20:04 the easiest way to sove that is by long division, you will get 1-1/(d²+1) which is trivial
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
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
"python can't do things like 420^71"
ah, you appear to have forgot about one of python's coolest features, unbounded sized ints!
"good morning fellow mathematicians, welcbaktnuda veedio"
accurate
This is unironically awesome practice for my test tomorrow as a calc2 student
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
I’ve never seen someone so excited to show off their integral collection
Awesome video :D
@ 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).
The collab i've been waiting for
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
“Take a deep breath such that you don’t laugh”
Dude, a great collaboration! Awesome to see you guys at it again!
Watching this video makes me feel like a complete idiot, but it gives me something to aim for in the future.
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
For small values of 420 it is approximately 0...
Seems legit
Integrate x dx. Everyone: it's x^2/2...
Him: let's substitute bs here and use e^some more bs.
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.
30:58 I am pretty sure this is just the area of trapezoid
it is way easier this way
30:54 Damn that's a surprisingly correct way to pronounce 'χ'
:)
@@PapaFlammy69 as a Greek I AM PROUD OF YOY
Jens and Andrew: *struggle when using common letters as variables*
Greeks: First time?
NOTICE ME PAPA FLAMMY
Holy canoli we have received yet another comedic addition to this lovely site
8:29 I think Dominated Convergence Theorem holds here - that’s why you can exchange limits.
19:40 For No. 9) you can do -> (d^2+1)-1 then split the integral and there you have it
I want to be as confident as Andrew!
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
Joke's on you, papa flammy. Python can calculate arbitrary large numbers, including 420^71.
f u c c
34:12 it's integral of x so you should use formula for triangle and rectangle area
8:31 it converges uniformly 😎
honestly, I was laughing more about how you calculated the integrals in Dotson manner, than about the memes :D
7:39 I never knew I needed to hear a german gentleman say "that ain't bad, at all" so much but here we are
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
28:43
"Eins... Epstein's theory of heat capacity"
Wtf!?!?!
daily reminder that heat capacity didn't kill itself
Andrew killed Epstein
you inspired me to use shitty variables for my math problems lol
Jens, at 19:37 you literally can add and subtract 1 in the numerator, then club them to be integral of (d^2 +1/d^2+1)-(1/d^2+1) dd. So then the first fraction gives d and the second gives arctan d after substituting d as tan d. Or you can do it the physics way which is remember that integral of 1/(d^2+1) dd is arctan d
more of these videos needed
you know, I'm a 16-year-old and I have no clue what is going on or why they're laughing so much but i like this part of youtube
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.
Make more of these videos they are great.
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
Oh I just realized you put Child of Light soundtrack in the back! Thanks, I love it
31:00 since pi = e = 3, then the result is 0 since we integrating from 3 to 3
You and Andrew are hilarious 😂😂 I cracked up every time Andrew had to say “approximately” when he had to integrate with respect to approximately. You guys should definitely do another one at some point.
@32:07 you can either use the gaussian trick or graph the function and calculate the area of triangle?!
For the problem at 30:18, could you take the definition of the definite integral to be the area under the graph of a function, and as such equate that to the area of the triangle formed under the graph i.e. 1/2bh ?
Literally laughed my ass off for nearly the entire video 🤣
:D
This humour is so niche, i dont know how i reached it but i love it
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?
The first integral is Coxeter’s integral. In Nahin’s Inside Interesting Integrals it was THE single, longest evaluation in the book.
Bruh this is so creative. LOVE IT
23:00 you could just add and subtract 1 in the numerator and separate it into 2 fractions
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))].
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
What an astonishing video, I should be studying, but YLYI is much better. Thank you for the entertainment.
19:50 use long division. d^2/d^2+1=1-1/(1+d^2) which is trivial
your voice on integrating the dd one makes it even funnier haha
24:40 integaral
Hello Papa Flammy ! I really love what you do on your channel ! This concept is soooooo cool ! If one day I want to reuse it, can I ?
Keep doing the great work !
15:40 This gave me PTSD of my mathematical physics complex analysis class back in university.
33:50 nice, I would've personally done it with a Riemann sum
I watched the whole thing. Loved every single part
That dd integral gave me a stroke
Flammy please do more of these, this could be such a good series
maybe with zach star?
9:01 if the variable runs from 42 to 419 then u cannot take the zero limit a contradiction
I enjoyed the video ! Isn't the one at 16:00 wrong because of the argument used but gives the right result ? For me, the denominator is nor even or odd function but the denominator - 1/2 is odd, so you can write the all thing it as even(x)*(odd(x)+1/2) so you just integrate the even part times 1/2 and it gives the same results. Cheers !
I genuinely think you would be the best Maths teacher of all time
Literally my conversation with another smart kid in the class.
Love the Forest Haven music in the background.
This video cured my depression , flammable maths laughing is the best therapy
Papa for χdχ just integrate by parts! Setting up the equation gives you int( χdχ ) = χ² - int( χdχ ). Add the integral to both sides and divide by two: You get χ²/2 ! :D
On integral #9, we could just use a quick long division on that ugly expression x² / (x²+1), we can turn it into 1 - 1/(x²-1) which is easy to integrate, it would just be x - arctan(x) + C :)