Integration Using a System of Equations

[@NPCooking69]

Can u hear the Engis scream, /tts uhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh. Thanks for watching, make sure to share the crap out of the video if you enjoyed it

[@PapaFlammy69]

fucc u

[@Gameboygenius]

@@PapaFlammy69 no flammy! no bulli flammy2!

[@a_llama]

lolol flamm2 dissing the og flamm

[@周品宏-o7w]

i think it would be better if g=-sinx , in order to make i+h=f+g and δ[f+g]=h-i or make -i+h=f+g and δ[f+g]=h+i

[@miguechiesa]

Theorem: if a number under 100 looks prime, it is prime unless it is 91.

[@PapaFlammy69]

yeye

[@Bobbel888]

You mean the only factorizable below 100 not covered by multiplication tables (

[@miguechiesa]

@@Bobbel888 yeah but this way it sounds more mystical

[@mastershooter64]

You mean conjecture?

[@miguechiesa]

@@mastershooter64 cross out the multiples of 2, 3, 5 and 11 (the easiest to check composite numbers). You'll end up with primes and 91

[@garvett6660]

Me: “walking with my headphones on” My friend: Hey man, what are you listening to? My headphones: “satisfying engineer screams”

[@PapaFlammy69]

xD

[@josephmartos]

Its nice that in the end, that artificial función i(x) doenst even show up and you got a nice formula that only needs the numerator to be the derivative of one of the denominator's functions

[@chiriviscospower]

It's not that deep bro

[@andrisgerasimovics812]

Why do you have a condition h = f'? You never use it in the proof and it restricts you to the choice i = -g' and hence a relation between f and g: f'-g' = f+g. The true condition for h for this method to work would be h = 0.5 (f+g+f'+g') but then you can derive the solution immediately.

[@tristanthepterodactyl2455]

Hi Flammable Maths, after viewing your videos for a year, I have decided to dedicate myself to being a full time physics stu... Ah shit wrong channel

[@PapaFlammy69]

May I introduce you to my basement?

[@tristanthepterodactyl2455]

@@aidankwek8340 Oh it's easy, it's equal to 3, which is coincidentally pi and e

[@peroperic4903]

Flammy, I suck at maths, I hated it in school, I struggled with basic functions. I studied languages because of my hate for maths, and 99% of the time I have no idea what are you talking about in your videos. But your delivery and enthusiasm are so intoxicating I can't help but watch every new upload, and I have been for the past few months. I know math is all about logic and building on previous knowledge, which I have none, except basic operations. I started with your videos about numbers, and I will slowly grind through the channel, trying to learn more. Keep up the amazing work, especially for us that have no clue about all this

[@jkid1134]

So, question: you establish three conditions on thr four functions f, g, h, and i. Could you then rewrite this entire thing in terms of one function, and then plug in various functions f to find a bunch of neat identities?

[@Cmummy]

The maths grind just does not stop 😎

[@PapaFlammy69]

:3

[@steve2817]

It's 11:15 PM here, and I watching math videos in bed. lol

[@PapaFlammy69]

Gud choice :D

[@tinnguyen2031]

Wow me too. It’s almost 11:00pm when I started the video... 😂😅

[@Observer_detector]

근데 저게 가능한 결과인가요? ㄷㄷ 이게 뭔 허무맹랑한 소리인가하고봤더니... 개신기하네요. 저게 된다고???

[@steve2817]

@@Observer_detector 대신 df/dx = h 인 경우에만 가능합니다.. 그래도 0~π cosx/(sinx+e^{-x^2}) 이런 적분이면 (π-π^2)/2 이렇게 바로 나오네요. 완전 쩌는 스킬인듯

[@Observer_detector]

@@steve2817 다시봐도 어이없네요 ㅋㅋㅋㅋㅋㅋ 헛웃음나오네 ㅋㅋㅋ 도대체 저런건 어디서 다 가져온겨 ㅋㅋㅋㅋㅋㅋ

[@joannaford7137]

An elegant solution,,,, custom interpretation and a powerful tool to deal with difficult integrands x

[@gropius6070]

I didn't know Germany had a 2nd Amendment -- is it only for mathematicians or does everyone have the right to bare arms?

[@Bobbel888]

Basically. You Need a License and Integrity references, about like a Driver license

[@ShazAndCo]

I have no idea what's going on but I appreciate the enthusiasm

[@patricius6378]

I can feel a monster approaching...

[@kepesmate6632]

The integral at the end is much easier to solve with making the substitution t=π/2-x, then adding the original integral to the new integral

[@atlasxatlas]

12:18 why did you bring the negative sign? it's part of h

[@blakejhonshen2710]

Super cool little formula that's actually pretty useful! And nice explanation!

[@nicolasmaillo2165]

Hi papa. After watching this video I started thinking about the consequences of this formula, and I'm clearly wrong on something lmao, but I don't know where. So say we had a function f(x) = a(x)/b(x) we want to integrate with some given bounds. Then we rewrite the bottom as b(x)-A(x)+A(x), where A'(x)=a(x). Write b(x)-A(x)= c(x) and we have that f(x)=a(x)/(Ax)+c(x)) where A'(x)=a(x) and we clearly know what c(x) is (I know that for many a's we cannot find A, but there are several cases where we can: linear combinations of exponentials, polynomials, trig functions,...) so we can then apply the formula. I mean, clearly I have to be wrong somewhere, please tell me what I didn't do correctly lol

[@martijntervelde5600]

It looks like a rather interesting method! But I do feel that to truly complete it, we'd have to substitute the function i(x) out of the conditions. This would yield a single test we can apply to any determinate integral of f'/(f+g). Some basic mathematics would then show us that this test is actually: f' - g' = f + g.

[@petersontaylor2000]

Agreed. And this test is actually solvable! f and g are good for that method iff f(x)= g(x) + 2e^x \int_0^x{ g(y) e^{-y} }dy Therefore, I think this is a very restrictive method... not that useful actually.

[@ramongallardocampos5241]

It makes me so fucking Happy The way you are so fucking Happy

[@PapaFlammy69]

:D

[@darkkyne6261]

i actualy solved this integral right before watching this video by adding and substracting 1 and then multiplying the integral by 2 and dividing it by 2 and i go the same result .

[@Ocklepod]

isn't it a requirement f(x)=/=g(x) for any x in [a,b] ? especially cos and sin don't fulfill this on [0,pi/2]

[@timothyrosenvall1496]

This is a really clever way of solving integrals for sure, but it's flawed. Due to the initial conditions, you only have one arbitrary function you can select, not two. Thus the fact that the final example with f = cos(x) and g = sin(x) comes out with the proper solution is completely coincidental. I wrote a brief stack exchange post on it here math.stackexchange.com/questions/3832174/papa-flammys-integration-using-a-system-of-equations

[@dimitris713]

I like how theres zachs head in the thumbnail just cuz he is an engineer lol

[@PapaFlammy69]

:D

[@Private_Duck]

Ooof I can feel the engineer pain approximating through my screen

[@elaceaceak2357]

I love that you did put zach in the thumbnail

[@ydg_me]

Using the property of integrals Its vay easier int(f(x)) from a to B = int(f(a+b-x)) from a to B

[@KillianDefaoite]

As always, thumbs up for Big Smoke. Keep big smoke in the vids and the thumbs will continue to roll in

[@PapaFlammy69]

will do :D

[@andre5032]

Lol my sister named her ginger cat "Flammy" after you...

[@PapaFlammy69]

:D

[@iambic-kilometer]

Given a specific f(x), it's fun to work out what g(x) has to be (up to integration constants).

[@Gameboygenius]

Engineers don't scream. They hover their hardhat and then calmly say "nope" before extending their neck up to the hat and rushing away.

[@souradeep3862]

Plzz try out this one in Papa's improvised session Integrate (1/2 to 2 ) arc(tanx)/1+x^2-x

[@tomkerruish2982]

I'm somewhat confused. You seem to be placing three conditions on the two functions h and i, which can't be satisfied in general, unless f and g themselves satisfy some condition, which I think is f + g + g' = f'. I'm sorry if I've gotten something wrong.

[@PapaFlammy69]

This identity only holds under the given conditions, that is right.

[@tomkerruish2982]

@@PapaFlammy69 Okay, thanks!

[@Reliquancy]

So does a choice of f(x) determine also what h(x) and g(x) have to be for this to work?

[@jackhanke343]

You also need f(a) cant equal -g(a) right?

[@CatDirac]

Why did you not put the absolute value to t in the integral of 1/t? Nothing tells to us that f(b)-g(a) and f(a)-g(a) are greater than zero

[@toaj868]

12:17 Shouldn't the negative sign not be there since it is part of h(x)?

[@HAL-oj4jb]

RI🅱 Jens 🅱ehlau

[@asliceofpi5933]

Flammy, it doesn't seem to work? The input of 0 to pi/4 for cosx/(sinx + cosx) should be [pi/4 + log((sin(pi/4) + cos(pi/4))/(sin0 + cos0))]/2 but wolfram alpha says otherwise by quite a reasonable, every integral I play about with usually doesn't work. Am I missing something in the theory of it n doing it wrong?

[@celost2025]

Isn't there a problem on the function i that you are using? i should be f+g-h and also derivative g = -i and in your case : i = sin+cos-cos = -g so it works but isn't this condition hard to come buy or am I missing something ?

[@Parodiaseharlemshake]

Papa, can you solve lim_{x -> 1} xsin(xpi)/ln(x^2 - x + 1) without L'Hospital's rule?

[@neilgerace355]

Arms reduction treaties don't apply to Papa 9:58 under the condition that 2 doesn't equal 0, which it doesn't because it is the successor of 1, if you trust the Peano axioms :)

[@PapaFlammy69]

:D

[@neilgerace355]

Zach the meteor hahaha

[@tszhanglau5747]

As a mathematician, I love this

[@abhishekkp7121]

Ah yes, another amazing question with amazing explanation. Keep on this good work man 👍

[@PapaFlammy69]

:)

[@jadegrace1312]

I think something is wrong with the conditions you gave, because otherwise int [a,b] 1/g(x) dx just becomes int [a,b] 1/(x+(g(x)-x)) dx=1/2*(b-a+ln(g(b)/g(a)).

[@aidanstanford6742]

Differentiation using torus decomposition pi-squared supermutated gaussian quantum linear homomorphism

[@anmolgupta-bj5ce]

Love your work 👏

[@PapaFlammy69]

Thx Anmol! :3

[@1stlullaby484]

Searched inflammable math got Flammable maths Edit: problems look good, new sub? :)

[@JB-ym4up]

If we look at 0 as 1-i⁴ we can see 0 factors into (1-i²)(1+i²).

[@Bloodsaberxy]

This means that by i^2 at -pi/2=-1 bruh... *shivers in e^(-i*pi/2)*

[@ashes2ashes3333]

I'm a bit confused how you define i here... on the one hand you require i = f+g-h, and on the other you require i = h- d_x f - d_x g = -d_x g. So does this technique only work for the special class of integrals where -d_x g = f+g-h? That seems a bit restrictive, and technically is not true for the example you give... what am I missing here?

[@timothyrosenvall1496]

I caught this two and posted a stack exchange link further exploring it. I think it's clever but not as useful as he's made it out to be because of these restrictions. Also his final example is incorrect because of this.

[@chan3912]

Papa Flammy is jacked as hell damn

[@PapaFlammy69]

:v

[@アナキンスカイオ一カ]

I think I should not be here, I am still learning linear algebra and analytical geometry. Even though I understand the principle of the integration and I know derivation. Whatever, I love seeing such these things.

[@ramanunnikrishnan7354]

Well then I am just out of high school and am not even some kinda prodigy, wdym

[@tamzidrahman2673]

That Zach Star face is why I am here

[@allliabdull6100]

Hey Papa Flammy Do you know when teespring is going to ship the clocks? I ordered two but havent recieved any by now.

[@PapaFlammy69]

Still not shipped out? I suppose production should end soon then and shipping should then begin then too!

[@theoreticalphysicist9241]

Yessssssss

[@sebastiian4002]

This is pretty nice papa! Luv u

[@PapaFlammy69]

Sebastian my son

[@aryandwivedi4875]

Papa am about start my university in about 10-15 days. In computer science can you please give me a word of advice please. 🙏🙏🙏🙏

[@akshaypr9164]

Jens!! why is it your symbol for differential becoming partial??? mathematicians get upset by that!!.

[@hammadsirhindi1320]

hey how can we solve such type of equations simultaneously for giving particular value to 'a' and 'b' solve x^2+y^2=a-----(1) x^3+y^3=b------(2)

[@EngMorvan]

Wow! That's a powerful technique! 🙂 And I'm just an engineer. 🙁

[@shreymaru1613]

I remember that a question based on the concept explained in this video was asked in JEE Advanced.

[@aasmoth]

Papa when will you be doing a summary of the Kobayashi Maid paper?

[@PapaFlammy69]

Soon actually XD

[@aasmoth]

@@PapaFlammy69 :D

[@yudoball]

Super smart

[@gianlucademarchi4401]

Wunderbar!!!!👍🏻👍🏻👍🏻👍🏻

[@mohak4275]

Going to use this in my exam

[@benjaminarias5193]

Papa biceps + Integharals = This is hot

[@mastershooter64]

You know what'd be a cool t-shirt? putting a(100 digit) long number on the t-shirt like divisible by a 4 digit prime number and calling it a prime number and you can say SIKE! just kidding it's actually not a prime it's divisible by this number and you can fool all your friends while you realize that you lost all your friends the week after you bought that t-shirt

[@mariangg2298]

Nice!

[@C-AbhijyotiKhakhalary]

Why do you guys like to call 57 a prime?

[@1stlullaby484]

Cause it's cute like you for example 🙄

[@The-wo4du]

When i see 57 normally it looks prime, that's why

[@olegmedwwed5947]

As far I can understand but you are wrong, mate. f'(x) = h(x) is NOT enough. And i(x) has not been included in general answer so any restrictions on it should not apply. Let's try to solve: Integrate {cos x /(sin x + x) dx} whatever interval u want. h(x) = cos(x) = f'(x). But ofc the result is not generalizing like u said. Pls, correct

[@raghualluri4245]

Damn Daniel! Very nice!!!

[@Observer_detector]

what a amazing result??????? is that equation really possible?? ohh..... i shocked lmao

[@integralboi2900]

Can you make a video on perfect numbers in Python?

[@krysen-VOD]

Cool

[@tobiasgorgen7592]

0:18 Despacito? Play Country Roads

[@tzovgo]

excuse me, sir... what's an application?

[@PapaFlammy69]

Something you can eat ngl

[@tzovgo]

@@PapaFlammy69 Sounds interesting; I'll be sure to try one sometime.

[@hernanfelipegonzalezaguirr7802]

I love you Papa, but please STAPH with that horrible notation of partial derivative. I'm crying in math, meanwhile physicists are enjoying our tears.

[@PapaFlammy69]

:'D

[@brendanlee1707]

Isnt the answer supposed to be pi/4 instead of -pi/4

[@brendanlee1707]

Yep oops, its -pi/4. Just checked wolfram

[@brendanlee1707]

But frkin awesome technique dude

[@PapaFlammy69]

:)

[@LuisBorja1981]

Sooo, it wasn't about approximations but about applications. Now I'm not scared by Zach... I'm kinda sorry.

[@thephysicistcuber175]

But papa, just use symmetry on the example.

[@txikitofandango]

12pi/e = 14 = 10 nice try

[@cuminmypapaya2239]

Bruhhhhh moment

[@PapaFlammy69]

*bruhv*

[@torment808]

hello my name is high level meth and I like to assume random bullshit things that somehow work :)

[@garvett6660]

Btw do you torture Andrew by constantly saying that not all matrices are invertible?

[@PapaFlammy69]

Nah, I just put *all* digits of pi all over the wall

[@garvett6660]

Flammable Maths Papa you’re a monster. That is genuinely inhumane.

[@ricardoparada5375]

Very interesting integration technique, I like it. 69th comment btw lmao

[@Pete-Prolly]

@0:28 wow, I never knew √(2)/2 = 1 Proof: cos(45) = √(2)/2 & tan(45) = 1 √(2)/2 = cos(45) = Syntax ERROR = tan(45) = 1 √(2)/2 = Syntax ERROR = 1 therefore √(2)/2 = 1 QED

[@alhusseinjamil7526]

No memes in maths please

[@amaro777_]

:v

[@swift3564]

690 views 42 minues ago lol

[@tsunningwah3471]

Team Fortress 2!!!!!!!!!!!!!!!!!!!!!!!

[@mudkip_btw]

Pretty tasty hmmm mlnlmmmlm