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Much efficient way to do is to substitute x = tan θ to get int(tan^4(θ)(1-tan(θ))^4 dx) and then can broken down easily into integrals of tanθ and secθ
@@PiyushPant-gy8sd Bro just to inform computers use newtons formula to calcualte and to be precise the binomial (1+x)^-n types idk exact but this is the method
@@ayush_5096 The ramanujan-π formula is an absolute beast and much beautiful than 355/113. However, the latter approximated ratio was originally developed not by ramanujan ( instead it was developed much years before him) . Further at school level , 355/113 is rarely used ( the simpler 22/7 is much more famous).
You could make any equation, with any limit, you should just be able to prove its positive and its value should be 22/7-π or some multiple of it, you dont need to remember that exact function
@@bobbybannerjee5156why not? We can take simple direct elementary functions such that we get 22/7- pi or pi - 22/7 and check whether the actual definite integral must be positive or not using graphs. This is a perfect derivation. At the end of the day, it makes sense doesn't it?
Actually, if we see what sir actually wished to convey how these two different problems were related and not exactly derive the solution...He just wished to make the students understand how any two branches of mathematics can be related and how beautiful this world of mathematics is...
Here's the problem with indian education which makes us lack capabilities to research. Research doesn't mean solving questions that are there in a book and checking your solution from the back of the book. That is what indian system has put into minds of most people when it comes to problem solving. Research is to analyse the problem, and come up with a solution that no one else has worked upon. Its stupid to say MIT students could not solve this problem. Ofc they could integrate this. Its just that its not obvious for anyone to come up with this integral on their own. "I know more digits of pi" yes, but the problem was to come up with the integral in the first place. That is something no indian would be able to do (perhaps no professors either at anyplace)... That's the tough part, not solving the integral.
You are 100% right, that is reason no innovation in IISc, IIT as compared MIT First of all comparing IIT JEE and MIT is meaning less. MIT intellectual property is countless, such a huge number of intellectual property rights. Well trained in JEE cracking is different from well education as well invocation mind Cracking JEE is well trained circus lion show Everyone is in unhealthy compitation(race) everyone busy, no time for improvement, no time to think.
@@AJ-fo3hp That's the problem with education in India now in my opinion. The unhealthy ratrace, competition, and online resources that claim to create "JEE crackers" and not "Intellectuals" causes students to miss out on the beauty of the subjects.
An Indian by the name,Madhav the first Indian to express pi as a series more than 700 years back. The man who should be credited to be the father of calculus. So please don't worry about Indian minds😂
Bro we don't need to take this function particularly. We can use easy functions ourselves to get this same value and compare right? That's all. Like for eg, we can just take the second last step of this video's integration
Approximate value of π was approximated by inscribing a unit circle inside a polygon Circumference of circle≤perimeter of polygon 22/7 is the perimeter of a polygon inscribing the circle π is the actual circumference of the circle Thus π
"Here education is like a food kept in a kitchen, not enriching the body of a person with nutrition." - Rabindranath Tagore (about one hundred years ago)
Instead of this if we use macclaurin expansion of tan inverse x it will give value of pi as a summation that will better define it instead of an averaged value because pi is someting that can be only defined by a given summation its my opinion anyone can share his/her opnion in the comment box i will be happy to know more opnions on pi
There is no compition between MIT and IIT, MIT is 100 times better than IITs, IIT teach you how to become good employee or ceo MIT teach you how to become good founder and entrepreneur
Incorrect There are actually more startup in IIt then MIT. But IIT got resevation so it lack in many unit ,and iit don't have that much good of teachers or research centre. But you shouldn't compare student of IIt to MITS in many Instance IIt students won major Olympiad,many startup are run by them ,and most of them are CEO. And year almost every unicorn in Indian are iitian own.
Ex 56 unicorn (self owned company with billion dollar revenue) are of MIT vs 91 unicorn are of IItians And there are many big companies of iitian are there . Don't listen to unemployed youtuber who didn't get admission in IIT so they are badmouthing IItians.
sir there is this integration which i have asked many people but no one is being able to solve this , it is not available online and even integration calculator shows error solving this. please please take this question , it has been more than 6 months but no one has given me its solution...... i have the answer but not the solution- the answer to the question is - Pi question- integration from -infinity to +infinity 1/(x^2-2xcotx+cosec^2 x) please sir solve this
In IITs, the education is mainly focussed on application not fundamental research.Though there are research scholars there who don't enter there through IITJEE
Sir I have a ❤❤ Question I see a video of🎉🎉 mind your decisions 🎉🎉channel Where they said 3rd root of (-1) and (-1)^(1/3) Are different things Please iske upar video banaayiye 😢😢😢
Alternate method for the integration: We can also use binomial expansion on numerator then divide the resulting polynomial (of degree 8) by x²+1 using long division method then integrate easily and we'll get the same result (22/7)-π
This is quite an interesting question if someone doesn't know quite a bit of the digits of pi (which doesn't have much use remembering) then it'd be quite a challenging question to solve given, you dont know the intergral that you have to solve.
Sir according to me its not a valid solution, its a kind of coincidence. How can the solution be developed if one doesn't have an idea of the integral?
Bro Solving the toughest problem would not make a student to invent something new we have to research about it.But our education system makes us employee not the entrepreneur.
Pata nahi kyoun, Par maine 11th mei hi maths chod ke physical education liya tha kyounki maths mere samajh se bahar thi. Par aaj mai ye maths ki videos kyoun dekh ra hun ? Jabki meri samajh mei kuch nahi aa raha. Utha le re bhagwaan ab to utha le.
I memorised pi = 3.1415926535897932384626433832795.. when I was in grade 7. That time the calculator in Windows 95/98 had these many digits after decimal 😅
But to answer that, one needs to be aware of the actual value of pi and 22/7. Tbh, who even remembers the actual value of pi? We take it as 3.142 after rounding while the actual value as you said is 3.141.
By iit or mit I mean students...the facilities you get in mit is much better than iit but students should a bit lower corresponding to the facilities they get
Aata to aapko bhi nhi hoga 1st time me aap bhi khi se chpka liye hoge to apne aap ko RUclips pr aake genius sabit krne ki logo ko aadat pad gy hai itne bade genius ho to aap bhi mit se paas out hote kisi chapri college se to nhi 😂😂
@@sankalp104 Its not calculated Mr It's basically Common sense 🤪 in our 7th standard teacher gave value of π upto 3 decimals So it's a piece of common sense 😃
@@erenbeggarverypoorBhai kha MIT or kha iit... comparison hi ni h... Noble prize ek b ni mila iitians ko ...or mit ne 100+ noble prize winners de diye hain ...kis hwa mein ho aap? MIT research krna sikhati h jo mankind k liye useful hai. Jo ki obviously startup krne se to bhut bdia kam h... Akele startup se comparison ni kr skte bhai aap... quality of education b dekhlo vha ki
What absolute Garbage. The true analysis is not about solving this integral,which is mundane and anyone with a practice will be able to do that. The true logic is how to come up with the problem in the first place. How did you expect anyone to remember that "integral question"? Where is the analysis part? In an analytical question you're supposed to start with assumptions of known fact,theorems and factual analysis. How did anyone would remember that mumbo jumbo?
Exactly. How did that integral come out from absolutely nowhere?? He's like asking people to remember that as some standard result. Like wtf would anyone remember that?
I was thinking same. I clicked on this video thinking how is he going find the equation to solve that? But here he just came up with an integral without any explanation 😂..
It's okay that student can't solve each every problem and MIT is something very different level university compare to our IITS which are just ridiculously old fashioned theoretical based course structure with lack of any innovation and motivation where as MIT focuses on solving the real life problems look to there research papers
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How to get you this types of problems sir. Please reply
Much efficient way to do is to substitute x = tan θ to get int(tan^4(θ)(1-tan(θ))^4 dx) and then can broken down easily into integrals of tanθ and secθ
Can you give full solution?
The most accurate value of π was given by ramanujan as 355/113 , we can easily compare 355/113 < 22/7
Ramanujan also derived a formula by which today's supercomputers has calculated the value of π after billions and trillions of decimal places
355/113 approximation is neither "most approximate" nor given by the great ramanujan. Further, 355/113
@@ibneabbas_2025 Checkout Ramanujan π formula, It's derived from there.355/113 is the simplest accurate value one can remember at school level.
@@PiyushPant-gy8sd Bro just to inform computers use newtons formula to calcualte and to be precise the binomial (1+x)^-n types idk exact but this is the method
@@ayush_5096 The ramanujan-π formula is an absolute beast and much beautiful than 355/113. However, the latter approximated ratio was originally developed not by ramanujan ( instead it was developed much years before him) . Further at school level , 355/113 is rarely used ( the simpler 22/7 is much more famous).
This is no derivation. Because it takes a problem to show it.
If a student had to prove that pi
You could make any equation, with any limit, you should just be able to prove its positive and its value should be 22/7-π or some multiple of it, you dont need to remember that exact function
@@aayushchhajed2630 True but that is not how you should do a derivation.
This strategy is relying on memory and experience, not mathematics.
@@bobbybannerjee5156why not? We can take simple direct elementary functions such that we get 22/7- pi or pi - 22/7 and check whether the actual definite integral must be positive or not using graphs. This is a perfect derivation. At the end of the day, it makes sense doesn't it?
@@ThorfinnBus How do you expect a student to remember an integral in order to show which is bigger of two given numbers.
Actually, if we see what sir actually wished to convey how these two different problems were related and not exactly derive the solution...He just wished to make the students understand how any two branches of mathematics can be related and how beautiful this world of mathematics is...
Me who remembers first 5 digits of pi 😅 : aao kabhi haveli pe
Me who knows first 15 digit 🗿
@@RoseGautam-sw6ly me with this pdf www.hebrewpi.com/1MillionPi-Digits.pdf
I know upto first 9 digits . Thanks to Google π game in calculator
Bina digits aur calculate karke batana tha
Same. I know 3.1415 but 22/7 is 3.142 so it is greater.
Here's the problem with indian education which makes us lack capabilities to research. Research doesn't mean solving questions that are there in a book and checking your solution from the back of the book. That is what indian system has put into minds of most people when it comes to problem solving. Research is to analyse the problem, and come up with a solution that no one else has worked upon. Its stupid to say MIT students could not solve this problem. Ofc they could integrate this. Its just that its not obvious for anyone to come up with this integral on their own. "I know more digits of pi" yes, but the problem was to come up with the integral in the first place. That is something no indian would be able to do (perhaps no professors either at anyplace)... That's the tough part, not solving the integral.
Absolutely correct, our system has so much hyped the answer rather than the process and solution, that's why we lack in research field.
You are 100% right, that is reason no innovation in IISc, IIT as compared MIT
First of all comparing IIT JEE and MIT is meaning less.
MIT intellectual property is countless, such a huge number of intellectual property rights.
Well trained in JEE cracking is different from well education as well invocation mind
Cracking JEE is well trained circus lion show
Everyone is in unhealthy compitation(race) everyone busy, no time for improvement, no time to think.
@@AJ-fo3hp That's the problem with education in India now in my opinion. The unhealthy ratrace, competition, and online resources that claim to create "JEE crackers" and not "Intellectuals" causes students to miss out on the beauty of the subjects.
sir second step by which rule.
An Indian by the name,Madhav the first Indian to express pi as a series more than 700 years back. The man who should be credited to be the father of calculus. So please don't worry about Indian minds😂
03:58 x-1 is not equal to 1-x. Wut u doing?? Please someone explain to me..
Directly open 1-x power 4 as whole sq of 1+x2-2x then again open whole sq directly (1+x2 ek term 2x ek term)then spit in fractions done🎉
Best approach
Nice explanation of the concept and method involved thank you so much for your time and effort.
How the student had thought ki is function ka integration karke prove hoga ?
Because usne tarun sir ka lecture dekha tha 😅.
Bro we don't need to take this function particularly. We can use easy functions ourselves to get this same value and compare right? That's all. Like for eg, we can just take the second last step of this video's integration
Approximate value of π was approximated by inscribing a unit circle inside a polygon
Circumference of circle≤perimeter of polygon
22/7 is the perimeter of a polygon inscribing the circle
π is the actual circumference of the circle
Thus π
"Here education is like a food kept in a kitchen, not enriching the body of a person with nutrition." - Rabindranath Tagore (about one hundred years ago)
Fantastic and Beautiful Prove . Hard touching concept❤❤❤❤
Heart Touching ❌️
Hard Touching ✅️
Hard Touching ☠
Instead of this if we use macclaurin expansion of tan inverse x it will give value of pi as a summation that will better define it instead of an averaged value because pi is someting that can be only defined by a given summation its my opinion anyone can share his/her opnion in the comment box i will be happy to know more opnions on pi
Bhannat sir
You are really the best
sir please off these glow when word glows we can not see clearly
Wait kya ye obvious nhi hain kyunki hame pata Hain ki 22/7 = 3.142 aur π = 3.141
Questions me bola gya tha ki calculus se solve Karo derive krke.
Ye jo hame value pata hai vo bhi to kahi na kahi se derive karke hi aayi hogi
Wese tum itne sure kese ho ki π ki value 3.141 hi hota hai?
Bhai calculator mai bhi check kr skte ho π = 3.1415
But 22/7= 3.1428
There is no compition between MIT and IIT, MIT is 100 times better than IITs,
IIT teach you how to become good employee or ceo
MIT teach you how to become good founder and entrepreneur
Incorrect
There are actually more startup in IIt then MIT.
But IIT got resevation so it lack in many unit ,and iit don't have that much good of teachers or research centre.
But you shouldn't compare student of IIt to MITS in many Instance IIt students won major Olympiad,many startup are run by them ,and most of them are CEO.
And year almost every unicorn in Indian are iitian own.
Ex 56 unicorn (self owned company with billion dollar revenue) are of MIT vs 91 unicorn are of IItians
And there are many big companies of iitian are there .
Don't listen to unemployed youtuber who didn't get admission in IIT so they are badmouthing IItians.
@@erenbeggarverypooraverage
IT labour defending iit ,🤧
@@Prince-9871 just an average labour
That didn't pass cbse trying to save his imaginary dreams.🤡
@@Prince-9871 I can see how much comment did you do to protect your downgrading steam.🤡
i had memorised value of π upto 100 decimals so it is easy to compare as 22/7 is 3.142 and π is 3.1415926....
How many iitian got nobel.amount,land infra, electric,food, library & per student spend on each student
They are it labour broo. 🤷
Just overrated fellows.🤦
How many Nobel you got
@@Prince-9871your English is more overrated 🤷
sir there is this integration which i have asked many people but no one is being able to solve this , it is not available online and even integration calculator shows error solving this. please please take this question , it has been more than 6 months but no one has given me its solution......
i have the answer but not the solution- the answer to the question is - Pi
question-
integration from -infinity to +infinity 1/(x^2-2xcotx+cosec^2 x)
please sir solve this
In IITs, the education is mainly focussed on application not fundamental research.Though there are research scholars there who don't enter there through IITJEE
Sir I have a ❤❤
Question I see a video of🎉🎉 mind your decisions 🎉🎉channel
Where they said
3rd root of (-1) and (-1)^(1/3)
Are different things
Please iske upar video banaayiye 😢😢😢
roots of unity
x^3-1 ko factorize krlo into x-1)(x^2+x+1) and then solve the quadrqatic part to get the three cube roots of 1
@@manishagupta587
Yaa I just slipped thank you
And by the way
Answer is
1,w,w²
Alternate method for the integration:
We can also use binomial expansion on numerator then divide the resulting polynomial (of degree 8) by x²+1 using long division method then integrate easily and we'll get the same result (22/7)-π
bro usme odd power bhi aayegi
@@kashishbindra hm toh?
@@kashishbindra usko bhi x² se toh divide kar hi sakte hena eg. x⁷÷x²=x⁵
This is quite an interesting question if someone doesn't know quite a bit of the digits of pi (which doesn't have much use remembering) then it'd be quite a challenging question to solve given, you dont know the intergral that you have to solve.
This is a problem from PUTNAM 1968 the profs who made the paper just took that problem from putnam and gave it in exam. No newness just copy pasting.
Sir i need full math course of math from beginning to advance level.Will u help me
I want to skip intigral calculus will it be good for NDA aspirants of arts background....
Naah
Just learn basic formula
That would be enough
Sir, ye prove krna Putnam Exam mein aaya tha( As far as i remember )
Yeah PUTNAM 1968
Sir second step smj nahi aay
There is no any fixed value of π its approximate or nearest value is 3.14
Question 2 min ka hai lekin chataai bichha kar 11 min laga diya
Fantastic Imagination
ek no sir mja a gya❤️❤️❤️❤️
gurudev achha feel nhi hota jab teu bolta hai to please o sound hta dijiyega next video se
*Here's a Harder question 😶
(1) π = 355/113
(2) π > 355/113
(3) π < 355/113
Prove It 🤨
Option 3
Option 2
Make an integral such that 355/113- pi comes that's all
@@ThorfinnBus maybe there are some other methods (EASIER)
@@ThorfinnBusthe audacity to say that's all
Thank you sir 😊❤😊
Every thing is linked with everything in mathematics, that's why we called it jwells of all subjects.
How can someone comeup with the integral part??
Anyone can fo this integration.you fid this because You already knew it .
Sir jee advanced 2021 ke paper 2 ka maths que. 5 bta dijiye
Sir according to me its not a valid solution, its a kind of coincidence.
How can the solution be developed if one doesn't have an idea of the integral?
When it comes to research work, there are universities in India that rank better than IITs
Good job but the integration method can only be understood by senior secondary students.
Good Question solved👍
Bro Solving the toughest problem would not make a student to invent something new we have to research about it.But our education system makes us employee not the entrepreneur.
Impressive.…job...
Nice tool for teaching
Sir Pin my comment:
It's known as Dallzel's integral it is the work of him appreciated
Pata nahi kyoun,
Par maine 11th mei hi maths chod ke physical education liya tha kyounki maths mere samajh se bahar thi.
Par aaj mai ye maths ki videos kyoun dekh ra hun ? Jabki meri samajh mei kuch nahi aa raha.
Utha le re bhagwaan ab to utha le.
Use wallis theorem
Parr humme ulta jaana hai. Humein function pataa hi nahi hai.
But here..... pi is the formation redian..... in this integral........
MIT is far better in all sorts of education facilities. It has no reservation schemes like IITs do where 50% seats are taken.
While MIT kept on giving to humanity IIT though tough hasnt much.
the reason why i remember pi 's value as 3.1415
Abhi to function chal rha h sirji😂
3.14
Correct
3.14
Iit continue making hard problems while mit students solve most of the word problems.
There was also a problem from a famous international olympiad(Putnam),the answer was π-22/7
द बेसिक डेफिनेशन से भी ज्यादा पी रेडियम इस इक्वल टू 180 डिग्री
I memorised pi = 3.1415926535897932384626433832795.. when I was in grade 7. That time the calculator in Windows 95/98 had these many digits after decimal 😅
pi to three decimal places is 3.141, 22/7 is 3.142; clearly pi is smaller than 22/7.
But to answer that, one needs to be aware of the actual value of pi and 22/7. Tbh, who even remembers the actual value of pi? We take it as 3.142 after rounding while the actual value as you said is 3.141.
Maturity is when you realize this sort of questions don't mean a thing..
Nice problem
himanshi world channel ne kal face revel krdiya
Sir like paid batch please make offline batch also
Jee mains 6 April shift 2
mains mai aaya tha kya ?
This is not a good apprpach for that problem though
π = 3.14159.....
22/7 = 3.142857....
Simply by comparing we can say
π
Math ke hero mera question hai
yet mit is more successfull than iit
No😂
@@IshaniRoy-v2kNo ? Are you drunk ? All IITs combined are nowhere near MIT or Harvard or Stanford.
By iit or mit I mean students...the facilities you get in mit is much better than iit but students should a bit lower corresponding to the facilities they get
Anyway we should focus on the problem not comparison
in science its never failure
Still IIT students will go in a company founded by MIT students😂😂
samay badlega😊
Because iitians are great employee and Mitians are greater employers
But Iitians making their unicorn 🤫
@@minecraftsmp1907kab bhai IIt 1952 se hai. Ab kab ???
Nhi badlega@@minecraftsmp1907
I like it.…
Thanks
Sir hats off to you kya jehar questions laye ho aur uska jehar solution ☠️💀 🔥❤
Good information❤
I could just do calculator
wowwwwww😍
Aap kaun si mit mei ho?
Maza aa gaya.
Aata to aapko bhi nhi hoga 1st time me aap bhi khi se chpka liye hoge to apne aap ko RUclips pr aake genius sabit krne ki logo ko aadat pad gy hai itne bade genius ho to aap bhi mit se paas out hote kisi chapri college se to nhi 😂😂
Pie is 3.141 and 22/7 is 3.142 so pie is less
Pi
@@sreevathsan246 ok bro chill
Calculator se calculate krke koi bhi krle😂
@@sankalp104 Its not calculated Mr
It's basically Common sense 🤪 in our 7th standard teacher gave value of π upto 3 decimals
So it's a piece of common sense 😃
@@pavansaiharshith2364 bro it seems ur in seventh standard till now-
What's pi ?
Haa maine iska video dekaa hai
How to block this bogus channel?
Unknown RUclips teacher comparing mit🥶 and iit🤡
A,b,c,d sunna jara 🤡
Teri sakal hi failure vali hai😂😂😂💀
It's just fact
Iit have more good startup earns more then MIT.
All the best for giving 50 lakh money in fees to MIT as a fees🤡
@@erenbeggarverypoorBhai kha MIT or kha iit... comparison hi ni h...
Noble prize ek b ni mila iitians ko ...or mit ne 100+ noble prize winners de diye hain ...kis hwa mein ho aap? MIT research krna sikhati h jo mankind k liye useful hai. Jo ki obviously startup krne se to bhut bdia kam h...
Akele startup se comparison ni kr skte bhai aap... quality of education b dekhlo vha ki
Hello sir
What absolute Garbage. The true analysis is not about solving this integral,which is mundane and anyone with a practice will be able to do that. The true logic is how to come up with the problem in the first place. How did you expect anyone to remember that "integral question"? Where is the analysis part?
In an analytical question you're supposed to start with assumptions of known fact,theorems and factual analysis. How did anyone would remember that mumbo jumbo?
Exactly. How did that integral come out from absolutely nowhere??
He's like asking people to remember that as some standard result.
Like wtf would anyone remember that?
I was thinking same. I clicked on this video thinking how is he going find the equation to solve that? But here he just came up with an integral without any explanation 😂..
Third one is correct 😊
Air 1 join mit
Option 1 and 3
youtube.com/@MATHS-BUDDY?si=edStWw-vGiWfcnDS sir is this your channel or a copied one ?
2
I dont know why I am feeling proud
Anyone love chess??
Yes, waiting for Gukesh vs Hikaru
What's your elo?
@@venom6221 Fide 1716 standard
It's okay that student can't solve each every problem and MIT is something very different level university compare to our IITS which are just ridiculously old fashioned theoretical based course structure with lack of any innovation and motivation where as MIT focuses on solving the real life problems look to there research papers
So high ego
Less than right
Kool iit wins