Integration By Differentiating Under The Integral Sign (HBD Feynman)

[@JewJon08]

I screamed out with joy when the natural logs canceled... it's a habit.

[@yourlordandsaviouryeesusbe2998]

@Intelligence Injection lmfao 😂😂😂😂

[@hiagoalves198]

me too. I felt like those girls reacting to kpop hahaha

[@knightvertrag]

Surprised you don't have throat cancer.

[@TheGoldenutz]

All engineering students feel your excitement 😂

[@cansomer6433]

Me too

[@astropartydan]

Great video. Thanks for giving Feynman props. In “Surely You’re Joking, Mr. Feynman”, Feynman talks about how he was always the integral guy at MIT, Princeton, and while working for Manhattan Project at Los Alamos. It came from his unique tool box of math tricks he learned from “Advanced Calculus” by Woods, which his HS physics teacher forced him to read since he was too talkative in class (because he was bored).

[@suvajitdey1101]

I today read about it and rush to KZbin to search for this this method...

[@bilalhussein9730]

@@suvajitdey1101 Read Smirnov's Course of Higher Mathematics Volume 2. It explains generally about integrals dependent on a parameter. Justifying the method rigorously requires the dominated convergence theorem but for applications no one bothers checking convergence.

[@suvajitdey1101]

@@bilalhussein9730 thank you friend.

[@ulfatahmad1354]

AA

[@chadwaldron3568]

Took Calc 50 years ago but I could still follow this. One of my profs said Calc will stay with you all of your life. I'm amazed.

[@AndrewDotsonvideos]

Like riding a bike? That’s awesome !

[@kalebbruwer]

I finished his book "Surely you're joking, Mr. Feynman" less than an hour ago, he mentions this in the book, so finding this in my recommendations was a pleasant surprise.

[@imonmahbub9515]

This video just made my integral life wayyyyyy much easier. Also really thanks to Sir Feynman!

[@TavoLL1511]

Lab partner: We need to calculate this integral asap! Me: Nah bro, just use the Simpson method.

[@GammaFZ]

or taylor approximate and then use the power rule

[@noway2831]

I love that I can finally understand one of your videos. Whenever you talk about nabla this and nabla that I have no clue what you're saying, but when you talk about pure maths everything clicks.

[@KeithJones-yq6of]

Great video, Mr Maths. Feynman was a genius physicist and probably one of the best teachers of science at every level EVER! He will live on forever

[@gavinriley5232]

Andrew you are my savior. I have spent hours trying to figure this out from professors notes for the final and you explained this amazingly

[@pabloAT98]

I have been a subscriber of you for a few months now. I was reading "surely you're joking Mr Feynman" and got to the chapter where he talks about this thing I hadn't been taught, so I decided to google it and found a video of you explaining it! Haha cheers from a physics student in Chile!

[@NazriB]

Lies again? Google Drive

[@MisterPeanutButter1]

This is so awesome! Feynman describes using this technique in 'Surely You're Joking'. I was very curious to what that technique was, even asked some teachers, but I never did find out. I very happy to finally know the approach!

[@restitutororbis964]

Isnt this practically just the Leibniz Integral rule?

[@AndrewDotsonvideos]

Yup!

[@tauhid9983]

@@Rahul-cb4jb Nah u don't get to say that!

[@roshanrajshah5817]

@@Rahul-cb4jb Fraud is very harsh word.

[@randomdude9135]

@@Rahul-cb4jb Physicists always like to take the credit of Mathematicians. Poor Leibniz isn't given as much credit for inventing calculus as Newton is. Eventhough both did indptly.

[@allaincumming6313]

Leibniz rule isn't normally taught. Feynman popularized it because he studied it from a book of an MIT professor, and he became locally famous among physics students for solving integrals that can't be solved by the normal taught methods.

[@ottod.g.6660]

I remember looking at this years ago - thinking it made no sense at all. I looked at it again today after being introduced to "Differentiation Under The Integral Sign" in my PDE class and gosh....it feels so good to understand how the heck this works.

[@AndrewDotsonvideos]

Such a good feeling. I used to watch videos way above what I could understand just because it was exciting to see what was around the corner. But then once you do understand it, for some reason it gets so easy to forget what was so hard about it for you in the first place. Do you remember what was unclear your first time around? Asking so I can put myself in those shoes better next time.

[@ottod.g.6660]

@@AndrewDotsonvideos I keep doing that continuously - even if you don't understand something clearly, at the very least you build up some familiarity. Well, I think what really confused me back then was how you re-defined the integral and how you jumped to differentiate it with a partial derivative. [Keep in mind that back then I only got exposed to Calculus I and was going on to Calculus II, so I had no idea what a partial derivative was]. I think you skipped one step (which is pretty obvious now but wasn't as obvious then to me - is more of a notation issue, I guess, since you do mention that you're differentiating g(x)) and that was how differentiating w.r.t. "x" can initially be written as d/dt Integral{0 to 1} (t^x-1)/ln(t) dt = Integral{0 to 1} partial(d)/partial(d)x (t^x-1)/ln(t) dt That was the only confusion I had really, the rest of it was just needed practice with integrals. Also, I really really appreciate your response and consideration - your videos have inspired me a lot on my path to staying in Physics. :)

[@lesnyk255]

I was never taught this method, and was completely unaware of its existence until I watched blackpenredpen integrate sinc(x) over the non-negative domain. It was a revelation! I love this method, it is sooooo cool!

[@pipertripp]

That's badass. A very cool technique to be sure. I'll have to find to practice examples to try it out on. Thx for sharing it.

[@gamma_dablam]

sin(x)/x

[@johnishikawa2200]

Awesome video! Even though I am rusty with calculus, I can still appreciate the elegance of this method, and maybe this is just what I need to motivate me to jump back into this material with both feet!

[@wumichael487]

It’s crazy when you just take a step back, and everything becomes so easy and clear.

[@danielburgess7101]

There was something really satisfying about your marker pens. Keep that up and you’ll have a fan for life.

[@AmigoRigo]

Because you're so serious in your jokes, being serious here makes me think you're joking

[@davidrittenhouse1774]

Surely you're joking, Mr. Dotson!

[@sandipanchatterjee5965]

😜Good one

[@yousiftop7605]

a year ago, i watched this vid and understood nothing (cuz was dumb). still dumb but with some more knowledge and the video was so helpful. thank you andrew.

[@rajendramisir3530]

Andrew Dotson, I like this integral you chose to demonstrate Dr. Richard Feyman"s technique. I admire the way you explained here in a clear, timely and patient manner. Thanks Andrew and Dr. Feyman.

[@vangrails]

And Leibniz, because Leibniz invented this.

[@humzahkhan6299]

My teacher was one of Feynman’s first students. It’s cool to see this video recommended like this. I have an exam tmrw wish me luck guys.

[@listentome5583]

Bro your handwriting is beautiful. Especially your “d”s

[@desudesudesu5326]

This isn't really a trivial result (not that you said it is, but some textbooks just assume you can move the limit in the integral) as I think you need the dominated convergence theorem to prove it. In that case, you have to check that the difference quotients of the integrand are bounded by a lebesgue-integrable function. Usually, they are if the integral is over a bounded domain and the derivative is continuous, because then you can use the mean value theorem to find the dominating function.

[@WizardCell]

You made my day! The method looks amazing. We learned it in class, but never understand it right as I did here! Thank you!

[@remixex369]

Something confused me, 7:21 why is g(x=0) the integral of 0 to 1 of 0dt?? Wouldnt it be the integral of -1/ln(t) from 0 to 1? Since you are replacing X not t, also that poses another problem, you are integrating the function for t=0 on a ln(t) which would be undefined, and also t^0 would also be undefined... Is it that trivial? Please tell me :(

[@MrPetrolhead007]

when you put g(x=0) the integrand becomes (t^0 - 1)/ln(t) but t^0 = 1 so the numerator becomes 1 - 1 = 0 so the integral is 0 so g(0)=0

[@pokechao196]

I was never taught this, so it's nice to finally learn this technique. I think there are some integrals I need to retry now...

[@aniruddhadatta8098]

Same here

[@ChristAliveForevermore]

Richard Feynman made this tidbit of advanced calculus quite famous. I printed out the PDF of Advanced Calculus which he used back then and lo and behold it was in there!

[@rmsvideos1335]

Does it work for indefinite integrals?

[@goose5996]

yeah for the last steps instead of subbing in the bounds to find g'(x), you need leave the integral as it is ((t^(x+1))/(x+1)), then integrate that with respect to x. whatever that comes out to be would be your indefinitely integral.

[@tedsheridan8725]

@@goose5996 Not exactly an easy integral to take. The problem in video only works out nicely because the limits are 0 and 1. For other values the exponent stays and g'(x) is no longer an elementary integral.

[@Soulheavenx]

It would be easier because you won’t have the upper and lower integral and you’ll have a constant in the end

[@simohayha6031]

@@goose5996 mostly only works if you have actual values in your integral sign. I saw one today integral from 0 to infinity of cos(5x)e^(-x^2) and it only worked using knowledge that 0 to inf of gaussian is sqrt pi/2. The actual primitive function involves error functions etc. This technique basically is a way to go around of non elementary functions to evaluate it to a number

[@joryjones6808]

Ted Sheridan I think the problem might be with is example because Integral( 1/ln(x)) aka Li(x) is a non elementary function.

[@Alan_Clark]

I have seen several videos of this technique on KZbin, but this is the clearest! Thanks.

[@edd.]

I love that technique!!! Great presentation!!

[@duncanw9901]

Great! Can you talk about this being a special case of the Leibniz rule for integration?

[@ゾカリクゾ]

yes I would really like that.

[@albertrichard3659]

Poor Leibniz keeps on getting his stuff stolen by physicists. First Newton and calculus and now Feynman and DUTIS.

[@theprince11]

Sup! That was a really good explanation. Can you please provide some more examples of where we can apply this kinda technique?

[@sss-ol3dl]

I tried it myself but used [(t^3 - 1) t^x]/ln(t) as the integrand. You get the same answer but have to consider g(x) as x approaches infinity to get the integrating constant. :)

[@nexus3112]

Watching him make sure the equation for integrating a to the power x was right multiple times in his head to make the vdo in one take was hilarious 😂

[@jakedones2099]

I love it. It is so nice. You differentiate with one variable and integrate with the same variable. I don't care who made it. It's genius

[@TheAnbyrley]

That was a great explanation of the method. Good work!

[@sungod9797]

Our advanced calculus professor gave us almost the exact same integral for one of our quizzes lol. It was integral from 0 to 1 of (x^2-1)/lnx, which is basically g(2) for g as defined in your video lol. So the final answer ended up being ln(2+1) = ln3 as the final answer.

[@meralsenses1376]

It was fun. I really enjoy watching it and I am going to watch it again. Thanks🙏😊

[@Strange_Quarks]

i love how i've watched this 3 times but still don't fully understand it yet

[@capitalist_cosmonaut451]

Thanks this is a great video on how to do Feynman integration really appreciate it.

[@Dexfire20]

Our university SQU recommends your video for independent learning 👍🏻

[@cottawalla]

One of the better explanations. Thanks.

[@ComarLantern]

I just found out this video 2 years later after it was uploaded and i am hopefully going to go to university next year to study physics. I have been watching your content for a while but i never went into the math videos because i am only graduating highschool and i only know how to integrate and how to take derivative of a function. I havent taken calculus but in Turkey our education system in highschool is a little bit harder. We take beginners level QM (basically starting from bohr and ending with coumpton event and debroglie wavelenght but no complex math we just learn the formulas and the philosophy behind them.), we take organic chemistry which was almost university level but now they simplified it a lot idk why it used to be like that glad that i didnt have to go through that lol. And we end math class with chamber analytics after we learn integral. Well as much as i know it was calculus level before but it was simplified couple of years ago. So i only knew integration techniques and ya know how to find an area under a function and some simple problems with integration/derivation. I dont know how to get an integral of natural log so i was curious about the video because those parts were cut out from our education system few years ago as i said. Soooo you didnt really need to know these but i just wanted to tell because i wanted you to know that i wasnt really at this level yet (even though its basic and i know some of it from my own research apart from school) and i really really enjoyed the video. You explained it really well and this was uploaded on feynmans bday unironically. I ejaculated after the ln(t)s disabled each other (jk jk). Thanks andrew, i love your videos! Greetings from Turkey!

[@dr.rahulgupta7573]

Excellent presentation of the topics in a beautiful manner. Thanks.DrRahul Rohtak Haryana India

[@AlchemistOfNirnroot]

Wtf just happened... Feel like the education system has been holding back *history channel alien music starts*

[@chymoney1]

Certainly not in the BC calc curriculum

[@mrnarason]

well partial derivatives are calc iii and i'm pretty sure BC calc only covers integrals and series.

[@chymoney1]

Victor P. concept of a taking the derivative with respect to x isn’t to daunting after a year of calc

[@mrnarason]

???

[@1999colebug]

I'm with you Victor, I don't know what they're talking about. I think they're saying partial derivatives (which they call taking the derivative with respect to x) aren't too daunting if you've taken a year of calc.

[@chymoney1]

Thats exactly what im saying

[@yashuppot3214]

Assum e=3 and proceed

[@sfundomabaso3200]

Lol

[@arbitraryconst]

5:24 What about the case if some x = -1? (I know, it's no element of the closed intervall from 0 to 1)

[@paulwirkus4182]

i honestly love your beard.

[@malenno9641]

Math tricks like these are so cool. Thanks for the video

[@piyushpatil4679]

This is one of my favourite technique.

[@weird407]

I have never seen this, but I remember applying something like this when I got stuck. Nice to know how it is formally done!

[@spencergee6948]

Talking at the camera (mike) and then at the board is like the scene from 'Singing in the Rain'!

[@markdatton1348]

Bro I'm in calc 2 and we just finished trig sub and did by parts, and I kind of knew vaguely about this but not really, and now I'm about to watch all the lectures cause that was neat

[@TavoLL1511]

Calc 2 also in here! 😆 Well, if your semester isn't already over (-__-)

[@billfeatherstone3018]

Thanks again very calm explanation is easy to absorb 😎😍

[@akankshasingh5749]

This was an awesome video and I love this method.Thank you.

[@fernandogarciacortez4911]

Awesome! After finishing calc I wanted to know some other methods, and since I always study physics, Feynman's was always mentioned in some of my books.

[@slothtv4991]

How do we know the integral of 0 is 0 if the derivative of any constant is 0?

[@mertokyay6401]

Hey man, love ur videos! But I have a question, this integral seems to be a type 2 improper integral. Why didn’t you evaluate as an improper integral?

[@ps3265]

I know the original integration went from 0 to 1 interval... Is this interval baked into the g'(x) and/or g(x) functions? I know the initial condition was used when he plugged in x=0, but I'm not sure when the end of the interval, i.e. 1, was used. Any clarification would be greatly appreciated.

[@ApiolJoe]

Same here.

[@paulboard8221]

You should do a review of the looks at the met gala it'll be fun

[@abramcaparaz3873]

Can you use integration by differentiating under the integral sign all the time, or are there any given conditions to use such a technique?

[@haryr_]

Could you have dealt with the logarithmic function in the denominator instead, and could have gotten to the same answer via Feynman’s method

[@kseniachernishov1904]

Would be nice if you'll make a video just solving integrals for a couple of hours :)

[@piboson6141]

Feynman is greatest physicist of all times.

[@SK-qc2hb]

T is the thing we will use to exploit the integral. WITH RESPECT TO T.

[@thomasblackwell9507]

Great video! Could you please do one on the derivation and proof of Feynman Technique of differentiating under the integral sign, please.

[@limitededition1485]

Didn't get why we put 0 to get c

[@cliffordwilliams9597]

WOW! So beautiful! Thank you!!

[@SandeepKumarDashSandeep12]

at t=5:24, How is the integration of t^x wrt t give me t^(x+1)/(x+1)??

[@chandlerkenworthy3185]

Absolutely brilliant video and explanation.

[@chessandmathguy]

8:25 and 8:36 why hold on to the abs value? Abs value of 4 is 4, so just ln4. :)

[@chamnil8666]

Great explanation,thank you so much

[@albertobermejo9557]

Hey thanks for these integrals videos they're being very helpful for my 2nd year in physics

[@Farcraft2]

what's the thing to look for when doing the choice of g(0)? Is it to get a constant C that's not function of 't' or any of x that makes it easy to integrate?

[@datitaniumduck9620]

Im probably late, but thanks for the vid bro, this helped me learn about Feynman's technique to integrate. It is out of portions for me currently, but it is interesting nonetheless.

[@parkinfurkmaz2877]

Is there a problem with evaluating g(0)? Just because one of our terminals is 0 and t ranges from 0 to 1, so integrand will have a 0^0 behaviour at lower limit (i.e. can we address convergence issues so that we can apply Leibnitz Integral rule?)

[@davidsuchodoll4124]

I´d like to mention, that you technically have to exclude x = -1... actually, it doesn´t matter in the end, since -1 is not part of the Integral Domain, but since this is planed to me for undergraduates - at least, that´s what I think, since you actually write down so many little steps - and missing out on excluding Values from the Domain in which you are Integrating is one of the most seen errors in undergraduates calculations, you can now consider it mentioned.

[@EngMorvan]

I love this method. 💙

[@daniellopez-vd8pm]

It was a grat video, but what properties must the function have to use this technique?

[@okaro6595]

Why are there absolute value around the 4?

[@marcioamaral7511]

Do you call every mathematical quantity a factor? Like the constant you added?

[@mrnarason]

No, "factor" implies its a multiple. A general word for mathematical quantity may be more like "term".

[@rmsvideos1335]

We call everything a factor in physics lol.

[@mrnarason]

Who's "we"?

[@rmsvideos1335]

Victor P. People in physics

[@marcioamaral7511]

You really shouldn't

[@TranquilSeaOfMath]

You did a nice job explaining this.

[@AndrewDotsonvideos]

Thanks!

[@claudefazio]

Excellent explanation!

[@111thisguy]

my calc 2 professor knew this would be too powerful to teach this

[@nosferatu5500]

Richard Feynman is my favourite physicist

[@drover7476]

This was such a class video well in mate

[@smokesmoker4301]

the substitution t^x is not properly described. Can you do it more detail? thx

[@pedromooregaissler6378]

I know it is technically the same thing but why not recognize that as the double integral of t^x where t is in (0,1) and x in (0,3)? It ends up being quicker than differentiation under the integral sign

[@michaelsalinger2134]

Super cool! Easy to follow as well

[@mrnogot4251]

This is why I love integration

[@mattRRgraham1996]

Hi, out of curiosity, if it isn't too much trouble, could you do another video with a more complicated integral for this process? I thought this was a great video (you really explained things well!!) and I certainly learned a new integration technique I hadn't encountered in my math curriculum, so I really want to thank you for that! I had been really eager to learn this technique for quite some time. However, my question is that this seemed like an integral that could have maybe been solved via integration by parts in a similar time manner. Perhaps this isn't the case, I admittedly haven't tried it via integration by parts, but I imagine there are integrals where this might be the only really feasible way of solving it. Sorry if this seems like a poor question, I have seen a glimpse of the power of this integration technique, but I'm thirsty for more! Looking forward to your series on Tensors as well. I wish math majors got to study tensors :(

[@AndrewDotsonvideos]

I couldn't figure out how to solve it using by parts! But I think that's a good idea. It is hard to set up the integrals at first.

[@carloingravalloba]

@@AndrewDotsonvideos However, I think that the comparison with the resolution method by parts is useful to do and can give indications that help to understand why this method is used and when it helps in the resolution in the sense that it facilitates it. In the part method you have two choices (= when to choose u and when instead v) and this depends on the resolution or ease of integration. In this case it should be that u = 1 / ln (×) and v is chosen for what remains.

[@Bronoulli]

Dude. Please do more videos like this

[@yamahantx7005]

Why are the bounds of g'(x) necessarily 0 to 1?

[@yoavwilliamson3378]

Interesting method! Very cool thx bro

[@BrennenBlack]

Why is it equal to the natural log of the absolute value of x+1 (ln|x+1|)? Why can’t we write it as ln(x+1), or is that the same thing and i’m just not familiar with it?

[@thaitrieu791]

Brennen Black if x

[@rhettwilson3616]

Which math class could I expect to see this in?

[@JivanPal]

Alternative way of doing the final step (after g' is found) that doesn't require you to find the constant of integration: g(3) = g(0) + \int_{0}^{3} { g'(x) dx }.

[@ph0non]

Am I stupid or shouldn't the Integral of 0* dt be a constant instead of just 0? Maybe my brain just isnt working rn idk