π^2/6 or ln(2), which one did you guys like more??

@MTd2

6 жыл бұрын

π^2/6, because it seems to have nothing to do with the integrand.

@olahalyn4139

6 жыл бұрын

yh (pi^2)/6. May I ask where is the circle hiding?

@TaleTN

6 жыл бұрын

ln(2), because it's more musical... :-p

@6612770

6 жыл бұрын

I love all of them!! You are an EXCELLENT teacher.

@hariskayani4703

6 жыл бұрын

blackpenredpen spoiler alert 🙄

Frullani had an integral and Leibnitz made a rule. Differentiation under the integral sign was Feynman's favourite tool

@PyarMatKaro

6 жыл бұрын

If we make the substitution u = ln x then the integrand becomes a fraction with u on the bottom. The result turns out to be a Frullani integral and the general solution to these can also be found with the trick that Feynman used, as shown in this video, where a parameter is introduced and the order of integration is changed. Evaluating it in this way would be a useful study exercise. Hint: consider the integral of e^-bu with respect to b

What a coincidence....!!!! Your video is of 14:58 mins, which is an interesting number.When its digits are added,the produces sum multiplied by its reverse give the original number.. 1 + 4 + 5 + 8 =18 and18 * 81 = 1458.There are only 3 non trivials number 81,1458 and 1729 (Ramanujan number 😊😊)...

@blackpenredpen

6 жыл бұрын

Wow nice. I did not plan on this one tho. But the previous one, yes.

@cubicardi8011

6 жыл бұрын

RAJ SINGH and the previous video length is 17:29 !!!!!!!!!!!!!!!!!

@palashagrawal1551

4 жыл бұрын

it is of 14:32...are u blind?

@Austin101123

4 жыл бұрын

0, 1, 81 are the trivial? Are there any others?

Wow, it's feels great after accidentally finding your channel.

@cpgrace1902

4 жыл бұрын

True

@nishatmunshi4672

3 жыл бұрын

True af

I absolutely love Feynman's Technique. has to be this one

@blackpenredpen

6 жыл бұрын

Taru nice pick!!

The approach with Feynman's technique is less familiar to me, so I felt I learned more. So, in terms of "which one I liked," I have to respond with the second one.

@blackpenredpen

6 жыл бұрын

I see!!!

@AndDiracisHisProphet

6 жыл бұрын

I agree. If you don't know what you could do next, some more examples of this would be nice. I guess.

Hi dear, In general case, you should check the conditions. For example, for b -1. Thank you for your videos and explanations.

This might sound weird, but you can perform a technique called "integration under the integral sign" here: you recognise 1 as x^0 and x as x^1. Remember the derivative of a^x is ln a . a^x. We can simplify the integrand to the integral from 0 to 1 of x^u du. Given the interval , we can switch the order of integration and integrate with respect to x first and the w.r.t u. This gives the result of ln(2) super fast!

perfect. differentiation under the integral sign is just amazing. if only there were more exames of it...

To be perfectly honest I like ln (2) more. Because I ve already known the result of the first integral since 2002. Thank Dr and keep going

both were amazing and what’s even more amazing is that i was able to do them both, which i didn’t expect at all

best and simplest example of Feynmann techniqe, I've seen many example of Feynmann Integrate but using complicated function (hard to understand for beginner)

Wait, I'm new to calculus and i think (x-1)/lnx is not defined at x =0 right, or we can just ignore that

What an interesting technique! I've never learned this! Thanks

My cat is also black & white. This version is cooler. Because of Feynman.

@blackpenredpen

6 жыл бұрын

AndDiracisHisProphet What's the name of ur cat?

Thanks for the video, I was stuck with my calculus assignment, exactly what I needed

I'm in love with integrals bcs of you thanks a lot. It looks hard but you simplify it.

I liked both techniques so much, so innovative. Awesome ideas!

@blackpenredpen

6 жыл бұрын

Thanks!!!!!!!!

Both integrals come out as nice series. Sum of reciprocal squares for the first one, and alternating harmonic series for the second.

Man, thanks a lot. Your channel solve some problems for me and motivate me to study math. Thanks!

@blackpenredpen

6 жыл бұрын

Luiz Felipe F M Costa this is great to hear!! Thanks!!!

真的很厲害！幫助了我很多，謝謝！Please keep posting those helpful and fun problems! You're amazing!

@blackpenredpen

6 жыл бұрын

不用客氣 我個人也很喜歡做這些題目!

yeaah part 2 won great well its impossible to figure out by looking at just integrals so awesome great work

So for b=e-1 The area is 1 :)

Very good explanation

Sir you saved my homework! thank you a lot!!!! was megahelpfull! =)

since ln(2) is the result of the alternating harmonic serie, is it possible to use the first method (or similar) to resolve the second integral?

More of these videos with this technique!!!

So good! This video was cool too, but I think I liked part 1 more tho

I tried this just from the thumbnail and I actually managed it, I genuinely can’t believe I did that!

very helpful video on integration topic

Very nice video! 13:10 the function isn't defined at x=0 which is one of the values in the integration.

Both are just amazing and so different in technique. Difficult to choose

This one! Great technique.

Both are awesome. So I like both equally.

You could also use the Laplace transform to solve this integral as well by setting ln(x)=-u. I would say I like π^2/6 more. When I first heard of it, I thought what does pi have to do with the sum of the inverse squares and why is pi squared?

The techniques used look quite clear (even I couldn't prove order of integral and derivative could be changed etc.), but too often it might be nearly impossible to see what technique to use.

This is a super interesting technique

How do we know that when we should use the Feynman's technique?

Cool! I am ashamed to having substituted and used the taylor series for e^u to get the alternating harmonic series.

So satisfying to watch

En qué curso se estudia la técnica de feynman?

Got this as a homework problem a day after you uploaded. Thanks a bunch!

@blackpenredpen

6 жыл бұрын

WOW!

@blackpenredpen

6 жыл бұрын

What class r u taking that u have to do this as a HW problem?

@frogger9801

6 жыл бұрын

PHYS 306 from Purdue University. It was assigned from Problem 2.2.10 in Shankar's "Basic Training in Mathematics". Screencap: imgur.com/a/DQuxQ

SO IMPRESSIVE

Feynman's technique wins this battle hands down IMHO. :-)

This is soooo good❤

I tried to calculate as f(a)=integral from ((x-1)/lnx)*exp(alnx), then f'(a)will be integral from (x-1)x^a, it's 1/(a+2)-(1/a+1), then I integrate it, I will get ln|(a+2)/(a+1)|, for a=0 I have the same result. Is it all right??

at 13:23 you talk about the 0/ln(0) = 0 but isn't that an improper intergral? Feels like we skipped a step.

Hey I use power series firstly i let u=lnx then i wrote down the integral in terms of power series of e^u then in the last i had to substitute infinity in that series and i was like blown up can u tell why did that infinity kinda thing happened...

I am watching this early in the morning at my breakfast befor going to university, and it realy sweeten up my monday morning XD

@blackpenredpen

6 жыл бұрын

nakkal seyyah nice!!!!

@yahyaguzide

6 жыл бұрын

😄👍

i am confus i tried to solve following integral by partial derivatives integral of e^-x*1/x dx like this i set first the integral i(t)=integral of e^-tx*1/x dx i applied next the derivetive with expect to t and i got -1/t*e^-tx so the derivative for t=1 is e^-x and the initial integral becomes -e^-x wtf ??? that's completly wrong becaus ethe derivetive of solution is totaly different by the function i integrated it in the beginig somebode could help me ????

Thank you so very much sir.

When you Calc I(0) from the definition you are taking x^0 as 1. But we know that the definite Integral is between 0 to 1. at x=0 we will have the indeterminate 0^0?

π^2/6 is amazing 😍😍😍

I suppose theoretical physicists keep coming up with this stuff when they get stuck on some crazy integrals in the course of their work. Feynman did so much for physics and still chips in with some new math. What a guy.

What happens if the power is -1? Does the integral not converge?

VERY IMPRESSIVE.

This is really cool.

Is c being 0 just in this case or always when using feynman technique

That was soo amazing...

Quick question: shouldn't we study the convergence of the integral first ? An then, I wonder how...

Brillant! I remember when you used this trick to calculate the integral on sin(x)e^(-bx) :) Could we get a general answer for integral from 0 to t of (x-1)/ln(x), saying I'(b) = t^(b+1)/(b+1)? Or it would be impossible to integrate?

@blackpenredpen

6 жыл бұрын

jeromesnail it works for 0 to 1 only. Otherwise the integral won't converge

@jeromesnail

6 жыл бұрын

blackpenredpen OK thank you!

But can I always put the derivation under the integration ?

Help with this integral: Integrate e^[-k*sqrt(1-x^2)] of 0 to infinity ; k>0

Love it!

OMG Awesomely :3 ... Can you make a 1vs1 battle?, for example, Dr. Peyam vs you integring some curious integrals. Love yah!

@blackpenredpen

6 жыл бұрын

Then we need to find a judge or something.. btw, he will beat me tho, i know it.

@7necromancer

6 жыл бұрын

The judge would be a clock, fastest wins!

@tanmacre

6 жыл бұрын

Yeah! ... Faster wins!, and U can make a really hard integrals with more people; idk, just for fun :)

@MarkMcDaniel

6 жыл бұрын

They would need a third party to come up with the questions, otherwise the one who made them up would know the correct path to the solution.

This is the first video from this channel which taught me something new.

It seems as if I was watching a Flammable maths video

Wow what a great math

Question: I was always taught the the Feynman method was easier. It seems like it takes a lot longer??

integration of 1/(x^2-a^2)^2 dx.can you do this?

Can Dr. Peynam or blackpenredpen do a proof/intuition/discussion of why the Feynman Technique works? Or a resource you can point to?

@vkilgore11

6 жыл бұрын

Btw I liked the first integral with (pi^2)/6.

@blackpenredpen

6 жыл бұрын

Barbee Island we will work something out.

@blackpenredpen

6 жыл бұрын

Barbee Island not sure when tho. Since we both of lots on our to-do list

@blackpenredpen

6 жыл бұрын

Barbee Island sorry

Finally I understood it

If we integrate I’(b) from 0 to 1 right away we wouldnt have to deal with the C, since the answer falls out from the ∫ₐᵇ f(x)dx = F(b) - F(a). Like this I(1) = ∫₀¹ 1/(b+1)db = ln(b+1)|₀¹ = ln(2) - ln(1) = ln(2), since we can see that ln(1) goes away. The method you show is safer in case we have an integral Where we can’t observe this

Amazing!

π^2/6 is my fav

Love it

Thx a lot dude! Now it makes click and bulb 💡 in my brain 🧠 is on! 🖖🏻🖖🏻🖖🏻🖖🏻perfect 😬😬😬

So nice

I like this one more than the other because I actually understood this, althought pi^2/6 is a more special number to me :)))))

I can't believe it took us so many centuries to figure this technique out.

@AndDiracisHisProphet

6 жыл бұрын

Feynman was just The Man!

when you cancelled out 0^(b+1), you have assumed that b+1>0. So no abs value is needed for ln(b+1). idk if this is correct :3

@kaishuro6156

4 жыл бұрын

Interesting , I think if we don't assume that and solve it both ways we could have 2 answers , like pie² / 6 and ln2

This one it's perfect ;D

Wait, why can’t I integrate by parts? Someone help.

gets me every time !

Feynman's technique is the best

I am taking calc 2 right now , I would like to know on which course will I learn those advanced integral techniques ??

@blackpenredpen

6 жыл бұрын

Honestly, I am not sure. I learned a lot of things on my own. Maybe perhaps in physics? Especially when you have to integrate sin(x)/x And I am sure others can provide their answers here too!

So are you deriving with respect to 1??

Do you believe we should teach Calculus students this technique at the end of Calc II? It wouldn't be hard to give a brief introduction to partial differentiation just so you can introduce multivariate calculus via this technique. It's a great combination of differential and integral calculus that goes a level deeper than the Fundamental Theorem of Calculus, don't you think?

I liked the power series but this one was good too

it's pretty good

I know that you addressed what happens if you have a bound of 0 with ln(x) in the integrand in the last video. My question is, when you're solving for C in this video, you get x^0 in the integrand, which is another problem when x=0. I know that lim x->0 (x^x) = 1, but it just doesn't feel right to apply that here. Can you elaborate on why this is okay?

@burk314

6 жыл бұрын

When dealing with the improper integral (lets focus on the problem at 0 and ignore the one at 1 for this), we technically turn it into the limit lim(a->0) int_a^1 (x^0-1)/ln(x) dx On this domain [a,1], we have x^0=1 with no issue. Therefore, we compute the integral, getting int_a^1 (x^0-1)/ln(x) dx=0, and then the limit of 0 remains 0. So, yes 0^0 is indeterminate, but we can basically side-step the issue.

@L1N3R1D3R

6 жыл бұрын

Thank you two for the explanations! I never liked using the improper integral format unless the discontinuity was in the middle of the curve, but I guess that's needed here.

@staffehn

6 жыл бұрын

Right.. improper Riemann integrals are another option. In my explanation I was talking about Lebesgue integrals, though. In both cases the point is that the boundary point 0 is not needed to be defined.

We need calculus3 also

Please integrate logX/1-x^2 ..please

both equally challenging

Alternating harmonic series vs the basel problem, your choice.

I preferred the integral in part 1.

This is great :D

@blackpenredpen

6 жыл бұрын

Thanks!!!!

It seems like Feynman technique can be treated as a result of interchanging the order of integration of an iterated integral.

9:56 is that not an error??? 1^(b+1) is not == 1 1^(b+1) = (1^b)*(1^1) THEREFORE its 1^b/(b+1) inside the integral?!

don't think i didn't notice the supreme flex