you prolly dont give a shit but if you are stoned like me during the covid times then you can watch pretty much all the latest movies and series on instaflixxer. Been binge watching with my brother for the last couple of months :)
1:45 isnt the dx missing for the first integral? Also awesome video :) With another powerful tool like this the battle against integrals is heating up xD
Integral can be calculated in following way limit (sum(cos(ξ)dt_{i}),max(dt_{i})=0) dt_{i} - length of subinterval of [0..x] ξ - is the value from subinterval [t_{i}..t_{i+1}] To avoid calculation of infinitely many values we can use theorem that for continous functions value of this limit is independent from interval divisions
Great technique, that will tame the beasty boi. Must remember that one, I would never have come up with it. From 3:00 onwards pretty straightforward, could write ahead of the video.
wow it is really cool trick. multiply on e^(-1/x) and swap x and -x when cos remains the same since cos(-x) = cos(x) you end up that the same integral is in form of e^1/x * cos(x) / -.-. then you add both versions of the same integral having 2I = integral of just cos(x)
By the way, TH-cam hasn't been notifying me of your videos even though I have the notification bell on. I wondered why you hadn't uploaded in a while and checked your channel to see you already uploaded 2 videos!
I understand very well why this very young german Professor Scholz earned the mathematical Fields Medal !!!! Congratulations !!! From Brazil . Ray Viana Sampaio .
I did it in a similar way. I broke it into two integrals, one from -pi/2 to 0 and another one from 0 to pi/2. In one of them, I made the substitution u=-x. Then, I used dummy variables to add it back to the other integral and then some stuff canceled out very nicely.
There was an easier way to combine the fractions than you did. If you multiply through the e^-1/x + 1 term by e^1/x you get obtain e^1/x on the numerator and 1 + e^1/x on the denominator. You can then add the two fractions together and obtain it all being equal to one.
a little problem for papa flammy : a/bc + d/ef + g/hi = 1 («bc» notation is not b times c but a number with 2 decimals like 65). You must find a,bc,d,ef,g,hi such as a/bc + d/ef + g/hi = 1
How can you integrate a function that is not defined in an interval? f(x) is not defined at x=0 and therefore not continuous. How can you integrate a function that is not continuous?
Integration is pretty chill about this sort of thing - probably the most extreme example is the unit impulse function, which has a zero value everywhere other than x=0, and is infinitely large at x=0, such that the integral across any interval that includes x=0 is defined as being equal to 1. To think about it more formally, there are two useful things that can counter the infinite effect of the discontinuity. Firstly, an infinitely large value times a differential element approaching zero can on its own converge towards a finite value if the function approaches infinity slowly enough. Secondly, a positive infinitely large value can cancel out a negative infinitely large value under the right circumstances. I'm not quite good enough with formal calculus to know which of these allows the method used in the video, so I'd welcome input from other comments, but I do know that integration typically copes relatively well with discontinuities in functions.
But I assume we can generalize this? We can replace e^(1/x) with any f(x) as long as f(x)*f(-x)=1 ? Can we for example replace e^(1/x) with e^(sin(x))?
The integral that started Mathvengers. I wonder what is going to be in Euler's game. Hopefully all of the mathvengers go back in time to stop Jens from killing this integral.
nice. can you make a video on finding volumes? i was trying to solve a problem in brilliant it was related to volume of a canoli. i ended up with some integral which i could not evaluate. there are some interesting applications of fubini's theorem in calculating double integrals.
I plugged this into an integral calculator and got "No antiderivative could be found within the given time limit, or all supported integration methods were tried unsuccessfully." lol
Hey papa, I know this request of mine will probably not be the most popular one but- Do you think you could make some of your calculus / linear algebra / trigonometry videos in German just like blackpenredpen does in Chinese (his own language)? Haha it’ll be very useful to Germans in your country who don’t speak English that well (if this subset even exist lmao) but I am mainly concerned about this: It’s summer now, I am nearly finishing my exams and want to get back to studying German, while also practicing my favourite hobby on my favourite channel 🥰 Also, whilst my knowledge of daily life German is pretty dayumn good, I consider moving to Germany in the future and if I ever do, it’ll be imperative to know some dieustshc =P
Can someone just explain this.....definite integration can be done over a range only if a function is continuous right?...and this function isn't continuous at 0
![What a crazy approach! Integral 1/(x^4+1) from 0 to infinity [ Papa Flammy's V2 ]](/img/n.gif)
The 4th link (unique decomposition) is not available, anyone else tried and didnt work?
Thank you mah boi
Flammable Maths Uh papa do you know where I could see the 2nd video? Its not working either and it looks like a neat technique.
you prolly dont give a shit but if you are stoned like me during the covid times then you can watch pretty much all the latest movies and series on instaflixxer. Been binge watching with my brother for the last couple of months :)
@Bishop Jared yup, have been watching on InstaFlixxer for since december myself =)
That integral was brutally murdered
DV just like England with football
You are one of the reasons I started to love maths so much in the last 12 months. Now I'm changing my degree to Math and Statistics this October
That function decomposition into an odd and even part is a really powerful tool.
papa flammy's technique > papa Feynman's technique
Can’t wait to see “10 ways to integrate cos(x)” 👌🏻
ja dann hau mal raus, haha ;D
Lol boi you had it coming
It's now at 22 or something, because of Mathvengers.
That was so beautiful. Almost... almost if it was planned all along :O
This was dank.
I need to take more notes in my Discrete Meme Theory class
This channel is straight up amazing
The production quality keeps getting better. Good work.
Thanks
1:45 isnt the dx missing for the first integral? Also awesome video :) With another powerful tool like this the battle against integrals is heating up xD
Integral can be calculated in following way
limit (sum(cos(ξ)dt_{i}),max(dt_{i})=0)
dt_{i} - length of subinterval of [0..x]
ξ - is the value from subinterval [t_{i}..t_{i+1}]
To avoid calculation of infinitely many values
we can use theorem that for continous functions
value of this limit is independent from interval divisions
That's a beautiful boi right there, thanks for the video
you're so high
high on maths
Ginger Stalin maths is a gateway drug to engineering. Join me.
No
No, engineering is a gateway drug to physics, and physics is a gateway drug to math
I started with Zach Star, which led me to physics, which led me to blackpenredpen and flammablemaths
This is beautiful
THIS IS LIT AF
Great technique, that will tame the beasty boi. Must remember that one, I would never have come up with it. From 3:00 onwards pretty straightforward, could write ahead of the video.
* S P I C Y B O I*
Beautiful Solution!
Papa - you simply rock. Keep it going Papa.
wow it is really cool trick. multiply on e^(-1/x) and swap x and -x when cos remains the same since cos(-x) = cos(x)
you end up that the same integral is in form of e^1/x * cos(x) / -.-.
then you add both versions of the same integral having 2I = integral of just cos(x)
I'm officially a patron Papa Flammy; keep up the good work!
Flammable Maths definitely a video too!
Flammable Maths just won't be able to submit one in time for flammyday :/
So much nostalgia... You dirty old boi...
papa Flammy never lets people down!
Quiet difficult way for a representation of the integral of cosx
that was so satisfying omg
“I should make a video on how to do this integral, I could probably come up with ten different ways.” TOP FIVE FORESHADOWING MOMENTS OF THE 2010S!!!
I love this channel.
By the way, TH-cam hasn't been notifying me of your videos even though I have the notification bell on. I wondered why you hadn't uploaded in a while and checked your channel to see you already uploaded 2 videos!
5:46 and integral war was born
I understand very well why this very young german Professor Scholz earned the mathematical Fields Medal !!!!
Congratulations !!!
From Brazil .
Ray Viana Sampaio .
Danke, Vater
Awesome video as always
I did it in a similar way. I broke it into two integrals, one from -pi/2 to 0 and another one from 0 to pi/2. In one of them, I made the substitution u=-x. Then, I used dummy variables to add it back to the other integral and then some stuff canceled out very nicely.
There was an easier way to combine the fractions than you did. If you multiply through the e^-1/x + 1 term by e^1/x you get obtain e^1/x on the numerator and 1 + e^1/x on the denominator. You can then add the two fractions together and obtain it all being equal to one.
This Integral are so easy to understand,i and easy to remember
Its a good rom com must watch
Mind blown!
One of the best you have done! And guess what, everything was formal lol.
great stuff my boys
Amazing solution! And this mathematician is as funny as hell.😂
Oh ja das video mit 10 arten des cos(x) zu integrieren klingt echt wie eine lustige idee😂
love it
Thank you, daddy. Give me more.
papa is so amazing
a little problem for papa flammy : a/bc + d/ef + g/hi = 1
(«bc» notation is not b times c but a number with 2 decimals like 65). You must find a,bc,d,ef,g,hi such as a/bc + d/ef + g/hi = 1
wow! nice development.
Wer hätte das gedacht! Cool.
f(x) from a to b = f(a+b-x), we can solve this with this method within 3 steps i think
This function jumps from 1 to 0 at x=0.
It seems like you can just add up the areas of [-pi/2, 0> and
what the amazing identity it is!
In Fichtenholz is similar decomposition for R(sin(x),cos(x)) integrand
This method is popularly known as ‘Taming the monster’
*Papa I miss you and your great Flammable Math*
*Please be more active, Papa*
Complete S U C C ess
The title is true. I'm pleased.
This is very interesting
:)
How can you integrate a function that is not defined in an interval? f(x) is not defined at x=0 and therefore not continuous. How can you integrate a function that is not continuous?
Integration is pretty chill about this sort of thing - probably the most extreme example is the unit impulse function, which has a zero value everywhere other than x=0, and is infinitely large at x=0, such that the integral across any interval that includes x=0 is defined as being equal to 1.
To think about it more formally, there are two useful things that can counter the infinite effect of the discontinuity. Firstly, an infinitely large value times a differential element approaching zero can on its own converge towards a finite value if the function approaches infinity slowly enough. Secondly, a positive infinitely large value can cancel out a negative infinitely large value under the right circumstances.
I'm not quite good enough with formal calculus to know which of these allows the method used in the video, so I'd welcome input from other comments, but I do know that integration typically copes relatively well with discontinuities in functions.
At x=o e^1/x is infinity. Cos(0)=1 then 1/e^1/x +1=1/infinity which is zero. It is well defined at x=0
yo what's the music for when you have the problem displayed at the beginning? it's so good! Also, keep up the great work man, love your videos!
That was beautiful... even though I don't know how to integrate...
Integrate x with 10 different methods😃
Oh my. I never knew Papa was a symmetry boy.
But I assume we can generalize this? We can replace e^(1/x) with any f(x) as long as f(x)*f(-x)=1 ? Can we for example replace e^(1/x) with e^(sin(x))?
The integral that started Mathvengers. I wonder what is going to be in Euler's game. Hopefully all of the mathvengers go back in time to stop Jens from killing this integral.
Now that's nice
You've got me shouting at my screen
nice. can you make a video on finding volumes? i was trying to solve a problem in brilliant it was related to volume of a canoli. i ended up with some integral which i could not evaluate. there are some interesting applications of fubini's theorem in calculating double integrals.
I plugged this into an integral calculator and got "No antiderivative could be found within the given time limit, or all supported integration methods were tried unsuccessfully." lol
:DDD
Well, this happened probably because integrand is undefined in 0
Mathvengers was born this day
Papa Flammy isn't there a problem with this integral cause f(x) isnt continuous at 0?
@@PapaFlammy69 f(x) isn't continuous but then f(x)+f(-x) is! What is this witchcraft
thx daddy ❤️
beautiful mind
thx for your videos ! great tricks :)
Hey papa,
I know this request of mine will probably not be the most popular one but-
Do you think you could make some of your calculus / linear algebra / trigonometry videos in German just like blackpenredpen does in Chinese (his own language)? Haha it’ll be very useful to Germans in your country who don’t speak English that well (if this subset even exist lmao) but I am mainly concerned about this:
It’s summer now, I am nearly finishing my exams and want to get back to studying German, while also practicing my favourite hobby on my favourite channel 🥰
Also, whilst my knowledge of daily life German is pretty dayumn good, I consider moving to Germany in the future and if I ever do, it’ll be imperative to know some dieustshc =P
so the next time someone asks "what is a 1?" they'll get this
Astonishing
Yes do the Integral 20 different equals!
You could just substitute u=-x and add the two equal integrals together. This is more straightforward and instructive I think.
Classic king
Daddy daddy can u gimmie some integrals with Bessel functions? I promise to be good!
nice method... thanks
Nice!
I would love to see 10 differents ways to Integrate cosine, pls do it!
Can someone just explain this.....definite integration can be done over a range only if a function is continuous right?...and this function isn't continuous at 0
Genius !
4k Mathematics
DOPE!
It's one of the most popular definite intigration question type in JEE Mains!👽
fuck JEE
Please show that sin(x) =sin(x+2Pi) with the taylor series of sin. Ps thats an absolute beast ^^
How can you say the symmetrical integral of the odd function is 0 if the function isn't continous on [-a,a]?
1:44 you missed a dx. Good remade vid tho.
Flammable Maths you're welcome, lel
At 1:55 you state that "this thing right here is an odd function". Why is that the case?
I see. Thanks Flammy
Flammable Maths if f(x)=cosx/(e^(1/x)+1) then f(-x)=e^(1/x)cosx/(e^(1/x)+1)=e^(1/x)f(x). What am I missing?
fmakofmako the odd function at 1:56 is just (f(x)-f(-x))/2
Koen Th thanks I misunderstood.
What are you planning to do after your degree?
Flammable Maths Of course, you are a natural :) What age group are you looking to teach? University-level?
Flammable Maths Holly shit, i wish i cold turn back time to go to school again, learn german and find you in order to have a teacher like you.
Flammable Maths Why not become a lecturer? You have the smarts
Whenever i see your face, it's automatically good day :)
at 3.00 how do you know that the integrand is even?
using the substitution t=-x also works well
hello! I have a math problem for you!
Integrate x^x^x^x^x... from 1/(e^e) to e^(1/e)
(an infinite tower of x raised to the power of x)
Isn't it integral from -pi/2 to pi/2 ? how did it become from 0 to pi/2 ?
'What the fuck are those?' ~not your average math channel