𝗖𝗮𝗻 𝗬𝗼𝘂 𝗖𝗿𝗮𝗰𝗸 This Tower Integral ? 😎 It is easy

Let's explore the special concepts that comes into play when solving questions containing tower of integration
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[@ayushmanchakraborty5744]

It is the golden ratio, i love how it just shows up everywhere you wouldnt expect it to be

[@vertechua]

Yeah....😅

[@gauravjindal1159]

A definite integral can have different solutions over different domains When we assumed the upper limit of the integral we specified a variable domain to the main integral hence we get different solutiona 3:36

[@FundamSrijan]

Solve kar diya khudse , easy tha . Ab kal doston par flex maroonga 😂

[@tbs_gc]

We are getting two answers because the essence of the definite integral is nothing but the area under the curve, in this question the upper limit is not mentioned which can either be positive or negative infinity that's the reason we are getting two answers. This makes more sense as the answers are not the exact negative of one another as the lower limit is 1.

[@Daiwik.]

Excellent logic.

[@Daiwik.]

@rameshrustagi2091 your logic is like saying 1/x^2 integration from 0 to infinity, should be infinity, as we cannot even visualise infinity, but we all know that the ans is some finite quantity. More over in quadratic questions where the power is extended to .... usually means to infinity.

[@tbs_gc]

@@Daiwik. Ichipaad Explanation!!!

[@ishansh0077]

What if the function was 2x^2 ? Then u would get 3 possible answers, what's ur reasoning about this ?

[@vertechua]

Does Phi (φ) play any role in this 'cause I see it everywhere I shouldn't.

[@akshatsharma1497]

sir the lower limit is one and the upper limit should always greater than one, therefore upper limit will be positive. since y=2x is a increasing function( a straight line with positive slop), so we can say that the value will be positive.

[@shrutibarnwal2059]

Same concept in physics : equivalent resistance of infinite ladder type question

[@AdIITyAJ]

Same ques. In basic maths as well as logs

[@jaadu2551]

​@@AdIITyAJ class 10 mei bhi hai

[@CR7RMJUVEMANU]

Bhai but ofc usme agar ek Negative hoga to reject kar denge .as resistance can't be negative.but Definite Integral can be both positive and negative.

[@sv0mega125]

Editor need a raise..what a colour grading and editings..

[@bkmishra7286]

Sir but definite integration, one of its definition is area under a curve right? then how is it possible for a function to have two different areas??

[@lakshay3745]

This is not the complete solution though, there are an infinite amount of fixed points of this function with the principal fixed points being phi and phi bar , this happens a lot when several other branches are ignored in an infinite iteration

[@stem7921]

Wait how do you get other solutions though?

[@lakshay3745]

If we evaluate this integral at phi or phi bar for that matter we know that f(phi)= phi so automatically f(f(f(f...f(phi) will also be obviously phi and same for phi ' but these are the principal branches, let's say any other number like -(phi) if you put f(-phi) you get phi and as we know phi is a fixed point so it will keep staying phi after that , there are an infinite amount of numbers which reach either phi or phi bar after a number of iterations and after it reaches there it becomes a fixed point, that's why there are an infinite amount of such points which eventually become fixed

[@stem7921]

Ohh that makes sense I forgot about other points which will eventually reach the golden ratio after some loops, thanks bro!! Vese date kab hai tumhari?

[@lakshay3745]

Np:) and 27 ko hai mera

[@DevarshBarevadiya]

Sir upper limit to lower limit se badi hi hoti hai to -ve vala root nahi le sakte dono ans nahi aa sakte sir.....pls reply me

[@mdasifeqbal2323]

Saw this type of problem on integration for the 1st time in my life.

[@naimtanvirnaimtanvir7348]

Sahi mein Maja aagaya ❤

[@ForStudy-]

Solved!! Easy one

[@mohitdeb2000]

The problem looks scary sir at first but it is actually very easy 😅 thank you sir gonna rock the exams with your and physics galaxy's help

[@AThousandSuns42]

Thanks sir, pls make a one shot on complex numbers

[@SaMaRTH_7061]

Sir isme newton lebnitz theorem lga kr diffrentiate kr de aur fir I ka value nikalne se nhi hoga aur agar nhi to kyu ???

[@Karthik-ry9bz]

Sir yeh quadratic mei kuch sawal mei series mei hota usmei y consider karke karthe hai difference hai poora😅😅😅😅😅

[@Ujjwalkumar-xp5sd]

❤ great maths teacher for me❤

[@vertechua]

There are 2 intriguing things about the question, 1- involvement of 'Phi (φ)' and the fact that even definite integration can have multiple answers 😮. Is it the Golden number that makes this problem so different? Edit: Each successive upper limit of the tower is the area under graph of 2x, should it tend to infinity?

[@vatsalkabra516]

Sir the upper bound of the integral is smaller than the lower bound if we put (1-√5)/2 Please correct me if I am wrong ❤

[@gauravjindal1159]

U can always change the upper and lower by use of negative

[@vatsalkabra516]

@@gauravjindal1159 ok thanks bhai

[@fanboyofshisho]

Solved in 20 seconds orally 💗

[@4m0d]

Sir maine ye question pehle dekha tha toh wahan kaha gaya tha ye integral tower defined hi nahi hai, kyoki iski ek value nahi hai

[@BHANNATMATHS]

Hahahaha

[@hemangsonara]

Sir can you pls explain the reson​@@BHANNATMATHS

[@alphapoint389]

Sir placement of equal sign should be towards below integral sign. Otherwise solution will be different. Thank you

[@Relax-rh9xg]

Sir ji mera pranam🙏🙏...mujhe question toh pyara laga hi saath me answer to aur bhi pyaara hai I.e. Golden ratio 1 + root5 /2...bole toh bhannat ❤❤

[@odio_stationofficial3420]

Even being in 11th, I was able to solve it, i.e. first "youtube" question ever that I solved lol😅

[@PanchalSahib-lh2op]

I am class 9 also

[@odio_stationofficial3420]

@@PanchalSahib-lh2op oh sorry I am in class 4th

[@PanchalSahib-lh2op]

@@odio_stationofficial3420 shi ma didi Meri memori weak h islia ma jee ki tayiyari abhi sa kr ra hu Islia muja y ata h

[@odio_stationofficial3420]

@@PanchalSahib-lh2op 😅 great 👍🏿

[@PanchalSahib-lh2op]

@@odio_stationofficial3420 ksm sa

[@subhamswer5620]

Sit this integration gives are of a symmetrical Graph which is not finite and take jumps the nature in increasing. .......substituton may be easy.

[@AnimesKaizoku]

It's a golden ratio

[@bluexwave5930]

My answer is 1/2 As y= int 1 to y ( 2x ) dx According yo labnize dy/dx = 2 ( y ) dy/dx - 0 1 = 2 y y= 1/2

[@atharvshinde88]

Best sir❤❤

[@hellfire8603]

I have been watching aman sir's video since a long time and as a result I have been able to solve this integral question even after I'm in 11th and not have studies this chapter thanks sir ....your online student Anuj Mishra

[@honestadministrator]

z = Integration ( 1 , z) [ 2 x dx ] z = z^2 - 1 z = 1/2 + √5/2, 1/2 - √5/2, here in z is golden ratio

[@milianxhighlights]

Sir agar ham iska graph sketch kare toh aur fundamentally dheke toh iska area joh ayega woh +ve quantity hoga agar y=2x me area under curve ko calculate karke toh joh area hai woh y=-ve area ke liye nhi hota toh iska answer (1+sqrt(5))/2 hi aana chahiye

[@vertechua]

Bro I thought that too, with the same reasoning. But if that was the case, sir must have mentioned it (instead left it up to us for brainstorming 😅)...

[@aravindakannank.s.]

i just watched it a few days ago in maths505 channel 😊

[@missionaryrav628]

Golden ratio 😊

[@Nemisanghavi1234]

Sir kya ham Y=Y^Y se solve nahi karskte ? Vaha se ans +1or-1 aa raha hai.

[@youtubekeloversearthindia2204]

What is the use of integration in visual mathematics,,,.... I am not understand the limits chapter and derivatives what is the visual uses of them

[@missionaryrav628]

To ace JEE

[@Ravi_choudhary7870]

Sir maine 1.5 min me soch kr solve kr diya ❤

[@kardam_ji512]

Sir pr definite integration me negative wala root reject kyu nhi Kiya?

[@adityadalai1304]

Sir aise sawal r d Sharma me kiya hai. And woh differentiation me tha jo kiya tha

[@omsam_arts3235]

Sir agr hum isme lebinitz rule laga ke diffrenciate krte he to answer 1/2 aaraha he... Sir please reply if you read it...

[@Sahil.YouTube.]

Sir, please bring the next lecture of Maxima and Minima 🙏🏼

[@Ajay_Vector]

Golden ratio

[@notrishy]

This is a question of infinity format. If you remember, we encounter similar questions in finding derivative. For example, y = x^x^x^x..... Find dy/dx. Same approach is used 🙏🏽🙏🏽

[@nitinagrawal4892]

can we say function must have been symmtric about x=1? @anyone@sir

[@saurabhvishwa1916]

Golden ratio ❤

[@NITISHKUMAR-gz8ol]

In this critical time... You have to solve previous years JEE question bcoz jee Mains is ahead...

[@naivedyam2675]

Ans is Golden ratio

[@jimutakumarpanda3877]

Sir can u please make a video on factorisation please😢,I am studying in class 9

[@hritamkashyap]

One of the answer is Golden ratio

[@PrajwalV1729]

Sir i🎉🎉😊😊 also solved it with same method ❤❤

[@gouravgupta1639]

Aman sir fav kuwadratic equation😂

[@uditraj5427]

Sir please class 10 ke liye ek series bana dijiye

[@Candy2006.]

Mera khudse hua👍🏻

[@asifi.h.1874]

Sir book ka nam bhi thoda boldijiye pls

[@minatibehera3803]

Sir ye toh inconsistent integral hai iske solutions infinite aa rahe hain

[@gulrezmathclasses2841]

In books se achchi mere pass books hai aapke friend Ashfaq sir ko pata hai gravity coaching wale ? ❤

[@hemangsonara]

Isko two parallel func satisfy karrahe hai aisa bol sakte hai?

[@PRScrewdriver16]

sir , x^X^8=8 vid ka ans ,x=8^1/8

[@shivanshnigam4015]

Sirji aap bhi Math 505 dekhte ho lag raha

[@experimentingalgorithm1546]

That guy is super OP

[@lakshay3745]

Yess I saw him as well

[@aadishaktiprasadaadishakti2927]

Sir 2^a(2a+1) = 4a ka solution hai kya ?

[@hackwithtechnoboy548]

insta se uthaya h na 😂

[@aadishaktiprasadaadishakti2927]

@@hackwithtechnoboy548 Mera Insta per account bhi nahi hai

[@aadishaktiprasadaadishakti2927]

@@hackwithtechnoboy548 You can't solve this question

[@hackwithtechnoboy548]

@@aadishaktiprasadaadishakti2927 it has no real solution kiddo 🤡

[@question9963]

Maine ans comment Kiya reply Karo sahi hai ky?o​@@aadishaktiprasadaadishakti2927

[@dhruvbhatia6808]

Aisa sawal sabhse pehle 10th Mai quadratic mai dekhne ko milta hai tbh

[@samiulshad6742]

I saw the same integral solution in Math 505 channel a week ago. The solution is actually wrong. A definite integral can not have 2 values. It converges to one value. Check out- kzbin.info/www/bejne/iGLWpHlqnrhmo80si=g9lwRlDq-8kjjBYL

[@lakshay3745]

I had seen that video before as well but and I agree that this solution is not fully correct not because the DI doesn't have 2 values but because it has an infinite amount of values, we need to find all the fixed points of this nested function and the principal fixed points are( phi )and( phi)" but there are also several other solutions which approach these two principal values after a finite amount of iterations

[@HarvanshSingh_]

yes i was going to comment the same thing

[@vishwassharma2006]

easiest question ever😁😁

[@SouparnaAdhikari]

Golden ratio.

[@Ashok-so5gf]

Kis kis ka exam 27 January ko hai 👍

[@Roysundramraj]

Mara

[@aryansaini4391]

Mera bhi

[@amongus-xq8lu]

Same here

[@bhavdeepsangwan3220]

29 ko h bro.. delhi

[@Lol-zw6dx]

😅

[@satyam-isical]

I already knew (1+sqrt5)/2=(1-sqrt5)/2

[@jst_rndm_uplder12]

im adding this comment before watching the solution 1 + - root 5/2

[@Jai_maa_karny]

Sir aap kaha se hai 😀 please reply 🙂🙏🙏🙏

[@nameka6127]

Are yr answer to bata do kya hoga dono me se

[@HarvanshSingh_]

Sir your solution is incomplete you only calculated two out of the infinite solutions to this problem your solutions are (1+5^1/2)/2 and (1-5^1/2)/2 lets call these φ and φ’ but if you notice you can put I= - φ or -φ’ and it will also be a solution This is because we cannot assume the entire upper limit to be equal to the original integral the upper limit can converge to φ or φ’ after any number of finite steps I cannot write the exact solution in the comments as it is very difficult to write mathematical symbols here but you can watch ‘Maths 505’ recent video in which he explains this integral in detail

[@lakshay3745]

Correct 👍

[@whyandhowdaushitenande]

I did it ✌️ if i can solve it then it means question was easy lol💀

[@AnshPathak2005]

easy question . bprp ne bhi karaya tha

[@Ayush-mg6xw]

Uske asan hi sawal hote hai usually lekin smjhata acha hai

[@AnshPathak2005]

Hmm...​@@Ayush-mg6xw bri the maths guy and 3b1b ke thode quality questions & concepts hote h

[@AnshPathak2005]

lekin bprp ka 100 integrals vali dono videos dekho . Ushme achhe questions kara rakhe h , maja aa gya ekdam

[@Ayush-mg6xw]

@@AnshPathak2005 dekha tha jab mai 11th mein tha lekin jee ke integration kuch alag hi hai 💀 question ho jate hai but usually lengthy

[@Bot-j9e]

War on 27th?

[@AlexalakMandal]

Sir maga a gaya integration kar ka😁😁😁😁😁😁😁😁😁😁😁😁😁🙂🙂🙂🙂🙂🙂🙂🔥🔥🔥🔥🔥🔥🔥

[@questionmark8326]

Ye to math 505 wala question hai

[@crackemjee-advanced8934]

Who want PnC revision like here 👇

[@vaibhavsingh5629]

The answer is only the positive one, we can see the lower limit of the integral, it is 1 so upper limit must be greater than 1, because we have solved the question assuming 1 to be the LOWER limit, and we know lower limit is always less than upper limit. Also any integral cannot have negative and positive area at the same time.

[@Ravis_funn_study]

Sir🙏🏼 (1+√5)/2 or (1-√5)/2

[@dixit....family...wonders110]

Class 9-10- 11-12 attendance here✋️ who want to Crack jee or maths related exams

[@sheetalverma5829]

Agar sach me hame exam se daar lagta to ham yha is wakt KZbin per na hote proud to be here

[@Jai_maa_karny]

Bhai aapka kuch dino me exam hai dar nahi lagta 😅

[@sheetalverma5829]

Nhi

[@DileshChaudhari-29]

Done

[@itz_shiva004]

(1±√5)/2

[@TMH2007]

Math 505

[@AnshPathak2005]

golden ratio

[@cooldude6940]

SIR WHY U R ALWAYS LEAVING EVERYTHING HALF U STARTED TEACHING IN PHYSICS GALAXY AND NOW U STOPPED TEACHING THERE ALSO WHYY SIRR

[@captainlevi5682]

Maths 505

[@R_D_X__777]

Thanks sir

[@bittombarman8207]

It was sasy

[@rajarshidas5287]

too easy ...it took me hardly 20 sec

[@PawanSingh-qd3dl]

kis kis ka exam 29 jan ko h

[@Kaju_katli_]

2 second me answer nikala 😤

[@santoshanand8661]

Me who solved this in mind even I'm in 11th. That's show how bhannat sir question quality decreases.

[@funny-vi4lk]

First viewer please pin me

[@VihaanKashyap-qi8he]

golden ratio