Boring note but at 4:06 it says I(t)=-1/(s^2+1) instead of I(t)=1/(t^2+1), maybe reminiscent of the use of laplace transforms for the integral. Anyway, fantastic video, awesome production quality! :D
The integration of the parametric function is such a cool topic I must say. It does simplify a lot difficult integrals such like ln(1+sin²x) from 0 to π/2 which is equal to π*ln((1+√2)/2)
That is because this is not calc 2 but advanced calc, semester 4 or beginning semester 5, senior level calc or leading to master level techniques for engineering.
It's Amazing how Feynman so frequently receives credit for this technique when it would actually attributed to Gottfried Leibniz. He wrote about it in a letter to Johann Bernoulli long before Feynman was even born. It seem a bit unfair to call it Feynman's Trick rather than the Leibniz integral rule. While Feynman was quite brilliant, he didn't invent this technique, he just read about it in a textbook when he was a teen and then popularized it when he was at MIT.
it's a bit annoying that Leibniz's rule keeps getting called "Feynman's method" since it far predates Feynman, and was well-known even in his time (despite what is sometimes claimed) -- it just so happens that Feynman has an unparalleled PR machine. good video tho
@@Chris.4345 My issue isn't that it takes away fame from Leibniz, my issue is, that as a matter of principle, people shouldn't receive credit for ideas which aren't their own. Science worships ideas, and proper title over them is a sacred thing.
@@flame0154Proper title over ideas is poison to science. It’s the worst part of it. Culturally, it’s important, since young people want to become like the famous thinkers before them. But to science itself, title over ideas is a hindrance. “Ipse dixit” is the most egregious example. It’s better if the title changes hands; it means someone checked it again and confirmed it wasn’t BS.
@@Chris.4345 Ridiculous comment. You're replying to the statement "people shouldn't receive credit for ideas which aren't their own". You think plagiarism is good? You think taking credit for something you had nothing to do with is good? How does it "hinder" anything *whatsoever* to attribute credit to people who worked hard and contributed something valuable? If something is a joint effort, and really the result of a community of people, then credit should be given to everyone who added something -- but that's still giving appropriate credit to people responsible for advancing those ideas. By the way, when we are not so strict about our adherence to this principle, it is mostly those "famous" thinkers themselves who benefit: people with the PR machine to take credit for other peoples work and get away with it -- like Feynman did, most egregiously with the path integral. I don't think it's useful to science when we form our understanding of our own history based on media spin.
@@flame0154”you think plagiarism […]” non sequitur. the rest of your rant is meaningless. a person or group of people receiving credit for a discovery is cultural currency, and is a defect of how science is conducted, not a feature.
Wait i see now think of it this way when you are integrating you are finding the area under function when you add e^(-tx) it initally seems like you are changing the function but since you evaluate the function for t=0 that contribution from e^(-tx) is going to be 1 for any value of x so in does nothing to affect the plot under the function. But imo there might be some flaw to this.
Im sorry but doing limits differentiation etc inside the integral is worth nothing without justification and for those who say that the justification is unnecessary, it represents 80 percents of the work when dealing with parameter integral. You can’t just skip this . Otherwise you never justify any convergence domain, any definition domain when adding the parameter t, and still, i think your video’s great , i just think people should be encouraged to be more and more rigorous and not just giving results like that :) for exemple , in the egg of sinx/x , you need to use dominated convergence theorem, the domination isn’t easy at all to find as sinx/X is only semi convergent!!
This method is indeed for those who are familiar with elementary integration... They then should also know why you can differentiate inside the integral, so the proof for it isn't required at all...
Well you’re not doing anything crazy tho, right? We differentiate but we also take note of that by saying I’(t). Which is why we need to take the integral after the fact
Do you really think that Feynman was the guy who invented this trick? This is ridiculous. Feynman was good in PR indeed. But he even did not understand that such tricks are actually the theorems, and these theorems have conditions to check. These theorems were very well known long before Feynman.
You clearly have no idea of what Feynman did, and what his work was about. He developed quantum field theory, where lots of hard integrals appear, and his methods simplified computations immensely. If you read books on the history of quantum electrodynamics you'll see that he did calculations in a few hours that took his peers weeks to perform. Indeed, he did not invent the trick, and never claimed he did. But he was definitely the first to realize its potential and apply it much farther than any of his predecessors. Would you object to people calling football a brazilian sport just because it was the english who invented it, even though not many people would be interested in the sport without the innovations they introduced? Just because someone had an idea 300 years ago and you developed it far beyond the original intent you don't deserve recognition?
I do not discuss quantum field theory, I discuss analysis. And yes, Feynman did claim that this trick was invented by him. You may find it on youtube. Actually in comparison with Euler, Laplace, Cauchy, Weierstrass he developed nothing new in this field. And once again: these are the theorems one must check the conditions under which they are valid.
@@olegzubelewicz3604 I literally have the Surely you're joking, Mr. Feynman book in front of me. He says he saw the technique in the book Advanced Calculus, from Frederick Woods. I just looked up that book, since it's public domain, and it's a small section out of many. Again, no one is claiming that Feynman was the first one to rigorously prove that you can switch the order of a derivative and an integral, and he wasn't the first to see it could be used to evaluate definite integrals either, but there's no doubt he was the first to use it as a practical tool that performs better than other techniques for lots of important integrals. And if you do the things Feynman was famous for, namely quantum field theory, you would conclude the same thing. Please respect the rights of other people if they think this contribution is more significant than proving some analysis theorem centuries ago, and refrain from calling it PR, as you are embarassing yourself.
@@olegzubelewicz3604 Well, while I understend what you are saying, I don't think that the statement of Feynman inventing the trick has a fallicy in it. He might have invented or "re-invented" it on his one without any previous knowledge about these type of integrals. Sometimes Physicists don't bother with theorems and such, because their concerns are different than those of mathematicians. However, I still agree, that the notion of this technique being established long before Feynman "invented" it, should never be ommited. It truly is annoying at times.
This method is NOT called "Feynman Integration" , IT'S CALLED *Leibniz Integral Rule* . Gottfried Leibniz DISCOVERED THE RULE, Feynman POPULARISED IT. THIS IS Leibniz's technique, NOT FEYNMAN'S. GIVE THE CREDIT TO THE RIGHT PERSON FOR GOODNESS SAKE 😡😡 0:29 - You meant, " With a little bit of help from *GOTTFRIED LEIBNIZ* " 😡😡
Channel aesthetics are awesome and the explanations are good too.
omg, can't believe it's you man! I just love your vids!
@@Brodosomemathskeep going bro.... insha'Allah you're channel will get the recognition it deserves.
Best video I have seen on this so far Love the visuals and hope you make more like this
literally the best frickin video on this topic and super fast too thank you so much
6:06 there's nothing more stupid in this world than using feyman's technique for integral 1/(1+x)^2 haha. Btw nice video
Amazing format! I love the video format. Great work brother ^_^ Keep shining 😎
Boring note but at 4:06 it says I(t)=-1/(s^2+1) instead of I(t)=1/(t^2+1), maybe reminiscent of the use of laplace transforms for the integral. Anyway, fantastic video, awesome production quality! :D
yeah I saw that too
Hi bro, please continue your Olympiad lectures course. I request you man, I really need those. And you're an absolute gem of a teacher.
The integration of the parametric function is such a cool topic I must say. It does simplify a lot difficult integrals such like ln(1+sin²x) from 0 to π/2 which is equal to π*ln((1+√2)/2)
What would you take as the parameter then ?
@@sparky2141 I solved it and got the same answer as Bruh-bk6yo by placing the parameter as a coefficient of the sin
@@Samir-zb3xk ohhh as in ln(1+ a(sin²x)) ?
Okay cool
Thanks Man
@@sparky2141 yea, it will require some trig identities and partial fractions but it will eventually work out
@@Samir-zb3xk Ohhh, sure
Let me try and see.
:)
This channel is a gem. I learned a lot.
based pfp
based pfp
OUTSTANDING explanation!
Crisp and to the point!
Really goo explanation, thanks!
Considered using Feynman instead of residue theorem on my complex analysis exam to do some real integrals lol
Neat stuff, clever techniques I was never taught in calculus 2
That is because this is not calc 2 but advanced calc, semester 4 or beginning semester 5, senior level calc or leading to master level techniques for engineering.
But what about for indefinite integrals? Is there any way to extend the rule for that?
Nice video!
It's Amazing how Feynman so frequently receives credit for this technique when it would actually attributed to Gottfried Leibniz. He wrote about it in a letter to Johann Bernoulli long before Feynman was even born. It seem a bit unfair to call it Feynman's Trick rather than the Leibniz integral rule. While Feynman was quite brilliant, he didn't invent this technique, he just read about it in a textbook when he was a teen and then popularized it when he was at MIT.
very good! mate😄
Very nice explanation!!
Feyman's method is used as a last resource to solve integrals which can not be solved simpler using other methods
it's a bit annoying that Leibniz's rule keeps getting called "Feynman's method" since it far predates Feynman, and was well-known even in his time (despite what is sometimes claimed) -- it just so happens that Feynman has an unparalleled PR machine. good video tho
If it’s any consolation, Leibniz is already culturally immortal. He can share a little of that with Feynman.
@@Chris.4345 My issue isn't that it takes away fame from Leibniz, my issue is, that as a matter of principle, people shouldn't receive credit for ideas which aren't their own. Science worships ideas, and proper title over them is a sacred thing.
@@flame0154Proper title over ideas is poison to science. It’s the worst part of it. Culturally, it’s important, since young people want to become like the famous thinkers before them. But to science itself, title over ideas is a hindrance. “Ipse dixit” is the most egregious example. It’s better if the title changes hands; it means someone checked it again and confirmed it wasn’t BS.
@@Chris.4345 Ridiculous comment. You're replying to the statement "people shouldn't receive credit for ideas which aren't their own". You think plagiarism is good? You think taking credit for something you had nothing to do with is good?
How does it "hinder" anything *whatsoever* to attribute credit to people who worked hard and contributed something valuable? If something is a joint effort, and really the result of a community of people, then credit should be given to everyone who added something -- but that's still giving appropriate credit to people responsible for advancing those ideas.
By the way, when we are not so strict about our adherence to this principle, it is mostly those "famous" thinkers themselves who benefit: people with the PR machine to take credit for other peoples work and get away with it -- like Feynman did, most egregiously with the path integral. I don't think it's useful to science when we form our understanding of our own history based on media spin.
@@flame0154”you think plagiarism […]” non sequitur. the rest of your rant is meaningless. a person or group of people receiving credit for a discovery is cultural currency, and is a defect of how science is conducted, not a feature.
beautiful!
A hidden gem of youtube? Sign me up!
bro, you teached!
cool video, make more
Gdzie studiujesz?
Something similar was used to add up all the natural numbers
ej Ty jesteś z PL cn? bo widziałem twoje tt z e8
omg this actually makes so much sense now
My mama seing my measuretheory book:
"Why have you spent two days nonstop on this book?"
"Just to justify interchanging two stupid symbols, mum" 😅
i lost him when he implemented e^-tx
I feel the same way.
Wait i see now think of it this way when you are integrating you are finding the area under function when you add e^(-tx) it initally seems like you are changing the function but since you evaluate the function for t=0 that contribution from e^(-tx) is going to be 1 for any value of x so in does nothing to affect the plot under the function. But imo there might be some flaw to this.
I would just stick to modifying my functions with functions only dependent on t
Im sorry but doing limits differentiation etc inside the integral is worth nothing without justification and for those who say that the justification is unnecessary, it represents 80 percents of the work when dealing with parameter integral. You can’t just skip this . Otherwise you never justify any convergence domain, any definition domain when adding the parameter t, and still, i think your video’s great , i just think people should be encouraged to be more and more rigorous and not just giving results like that :) for exemple , in the egg of sinx/x , you need to use dominated convergence theorem, the domination isn’t easy at all to find as sinx/X is only semi convergent!!
Everything is great but what if any sis was doing math?
Ho, very well explained!
Watching this after finishing college apps. What am i doing 😭
edit: I dont even need to know this
your proof isn’t worth anything if you don’t justify why you can differentiate inside the integral !!!
This method is indeed for those who are familiar with elementary integration... They then should also know why you can differentiate inside the integral, so the proof for it isn't required at all...
Well you’re not doing anything crazy tho, right? We differentiate but we also take note of that by saying I’(t). Which is why we need to take the integral after the fact
You basically need uniform convergence for I'(t) and by point convergence of I(t) on some set T
It's really important to know!
It depends. In my country, you always have to justify it. Maybe in other countries you dont need to be as rigourous
He’s not proving anything dude. It’s a 6 minute video introducing the idea. He isn’t gonna get specific
You are too hary. Use board and pen to get the information.
Anyway nice example ❤
Do you really think that Feynman was the guy who invented this trick? This is ridiculous. Feynman was good in PR indeed. But he even did not understand that such tricks are actually the theorems, and these theorems have conditions to check. These theorems were very well known long before Feynman.
You clearly have no idea of what Feynman did, and what his work was about. He developed quantum field theory, where lots of hard integrals appear, and his methods simplified computations immensely. If you read books on the history of quantum electrodynamics you'll see that he did calculations in a few hours that took his peers weeks to perform.
Indeed, he did not invent the trick, and never claimed he did. But he was definitely the first to realize its potential and apply it much farther than any of his predecessors.
Would you object to people calling football a brazilian sport just because it was the english who invented it, even though not many people would be interested in the sport without the innovations they introduced? Just because someone had an idea 300 years ago and you developed it far beyond the original intent you don't deserve recognition?
I do not discuss quantum field theory, I discuss analysis. And yes, Feynman did claim that this trick was invented by him. You may find it on youtube. Actually in comparison with Euler, Laplace, Cauchy, Weierstrass he developed nothing new in this field.
And once again: these are the theorems one must check the conditions under which they are valid.
@@olegzubelewicz3604 I literally have the Surely you're joking, Mr. Feynman book in front of me. He says he saw the technique in the book Advanced Calculus, from Frederick Woods. I just looked up that book, since it's public domain, and it's a small section out of many.
Again, no one is claiming that Feynman was the first one to rigorously prove that you can switch the order of a derivative and an integral, and he wasn't the first to see it could be used to evaluate definite integrals either, but there's no doubt he was the first to use it as a practical tool that performs better than other techniques for lots of important integrals. And if you do the things Feynman was famous for, namely quantum field theory, you would conclude the same thing. Please respect the rights of other people if they think this contribution is more significant than proving some analysis theorem centuries ago, and refrain from calling it PR, as you are embarassing yourself.
@@olegzubelewicz3604 Well, while I understend what you are saying, I don't think that the statement of Feynman inventing the trick has a fallicy in it. He might have invented or "re-invented" it on his one without any previous knowledge about these type of integrals. Sometimes Physicists don't bother with theorems and such, because their concerns are different than those of mathematicians.
However, I still agree, that the notion of this technique being established long before Feynman "invented" it, should never be ommited. It truly is annoying at times.
This method is NOT called "Feynman Integration" , IT'S CALLED *Leibniz Integral Rule* .
Gottfried Leibniz DISCOVERED THE RULE,
Feynman POPULARISED IT.
THIS IS Leibniz's technique, NOT FEYNMAN'S.
GIVE THE CREDIT TO THE RIGHT PERSON FOR GOODNESS SAKE 😡😡
0:29 - You meant, " With a little bit of help from *GOTTFRIED LEIBNIZ* " 😡😡
well deserved dislike
not useful
Considered using Feynman instead of residue theorem on my complex analysis exam to do some real integrals lol