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great vid mate

I had to regretfully stop watching your video because the music required too much of my awareness.

I quite enjoyed that. Well done 👍.

I realized that I reached the end of the video...Feynman/Chopin - worked well! Many thanks!

I personally loved the background music, helped me concentrate.😊

Best video I’ve ever seen

I did this for a school project, I found the solution in a paper by Keith Conrad if anyone is wondering where

Next e^((-x^2)/2)

I find the music refreshing

f(0) =N*Pi/2.....so if should contain infinite solutions

HELLO DUDE GUD VID I ALSO LIKE THE MUSIC KEEP GOING

I personally would like this video without music, as a musician i find it annoying. my brain keeps telling me to listen to the music.

What application is being used to write on?

I was always taught , in the absence of x or ln, that e would be chosen as u in integration by parts. But it gives the same result.

Time very well utilized watching your program. Now to put it on paper and see how far I understood u.😮

Solved easily with Laplace transform

Can Feynman's technique be applied to any integral? if not, what are the conditions for it to be applied, please?

You sound so honest and at the same time hilarious making the video worth to watch

Double integration is my favorite method...

A da is missing from the left-hand side of several of the steps. Apart from this, it’s pleasurable to follow the process.

Nice application of the Feynman technique. The background music sounds strange and is a distraction under accelerated playback, so maybe it can be omitted for future videos.

Very easy to follow. Good job! Keep em coming!

Please make videos on sieve theory

Thank you bro loved it

The reasoning about I'(a) re lim_{t->oo} isn't true if a is zero. This seems like a problem.

Very cool.

It is amazing that someone would keep playing with that until you get to the answer. I'm impressed. I think the 3D version is much easier to grasp, using infinitesimal rings, but this is more impressive in some ways.

Good. But as a musician i suggest to turn off music. I cannot resist to pay attention to how Chopin Is played..

I am glad you made the effort to write out every step! Awesome!!!

Quantum Field Infinities Contradictory: Quantum Field Theory Feynman Diagrams with infinite terms like: ∫ d4k / (k2 - m2) = ∞ Perturbative quantum field theories rely on renormalization to subtract infinite quantities from equations, which is an ad-hoc procedure lacking conceptual justification. Non-Contradictory: Infinitesimal Regulator QFT ∫ d4k / [(k2 - m2 + ε2)1/2] < ∞ Using infinitesimals ε as regulators instead of adhoc renormalization avoids true mathematical infinities while preserving empirical results.

I think this is the best method of solving the Gaussian integral!!

You 'only' need to guess the right auxliary function to integrate and 'just know' that (arctan x)' = 1/(1 + x^2). Yes, yes, differentiating inverse trig functions is nothing compared to guessing convenient auxliary problems to solve. I'd call it: Gaussian integral made even more difficult. 😁But hey, a very nice video.

Interesting, but before destroying anything about Gauss they must first get near to him.

It’s beautiful. A small correction, you need to state a>0, otherwise it does not follow the limit of u as infinity.

why is feynman zesty in all your video?

Hi! That was a great video. I had a question @ 5:19, How should one go about selecting what function to use if they're trying to solve an integral for the first time with feynman's technique?

ballade no 1!

Wonderful.

Sorry for the music being a bit loud 😅

what app is this?? the one u are writing on??

Use Feynman's trick let I(a)=int_0^(oo) [1-exp(-ax)]*exp(-x)/x dx I’(a)= int_0^(infity) exp[-(a+1)x] dx=1/(1+a) I(a)=ln(1+a)+c, I(0)=c=0 I(a)=ln(1+a) # The general form is int_0^(oo) [exp(-ax)-exp(-bx)]/x dx =ln(b/a) Original question can rewrite int_0^(oo) [exp(-x)-exp(-(1+a)x)]/x dx =ln(1+a)

I love obi wan teaching me calculus!

Sin x = 1/1! x - 1/3! x³ + 1/5! x⁵ - .... So sin x /x = 1/1! - 1/3! x² + 1/5! x⁴ - .... And the I tergal is just : ∫ Sin x/x . dx = 1/1! x - 1/3! x³/3 + 1/5! x⁵/5 - .... + (-1)^n 1/n!. x^n /n +... You can also integrate many functions including the naughty function f(x)= e^x² which is otherwise does not have an explicit formula of integral. Off course with a condition of being an analytic function.

Integral of sin(x) / x dx from 0 to infinity is a classic. Here's an algebraic approach. It does extend into the patterns of series, binomial theorem - identities, as well as the complex plane: This may not be a complete proof or solution, but it illustrates the point. I find this to be another decent approach towards evaluating or trying to solve it. Setup and a few basic common principles: Not all of them may be directly used but are good and useful to keep in mind. Slope-Intercept form of a line y = mx + b. Slope formula: m = (y2-y1)/(x2-x1) = deltaY/deltaX = sin(t)/cos(t) = tan(t) where t is the angle theta between the line y = mx+b and the +x-axis. Initial Conditions: m = 1, b = 0. Constraints: b will always be 0. Simplification: y = 1*x + 0 <==> y = x. Substitutions: y = mx == y = sin(t)/cos(t) * x == x * tan(t). We can write this as sin(t) / t. The thing to recognize here is that the integration here is in relation to the angle, as opposed to the x - dx form. We know that 90 degrees or PI/2 radians is a Right Angle. We know that, multiplying by the imaginary unit i vector has the same exact effect of rotating by 90 degrees and by multiplying any value by i^(4*N) where N is an +Integer is the same as multiplying by 1 since it rotates it by 360 degrees or 2PI radians. Taking the graph of this function and looking for the area under the curve can be broken down into intervals based on the properties and relationships between PI/2 and i within the context of the summation of their series that converges to PI/2 or 90 Degrees. The Series: n=0 |--> +infinity of: (2n)!! / (2n+1)!! * (1/2)^n = PI/2 The double factorial (!!) is define by 0!! = 1!! and n!! = n(n-2)!! Then: f(t) = Series: n=0 |--> +infinity of: (-1)^n / (2n+1) * t^n Note that f(1) = PI/4. We can take the Euler Transform of the series: 1/(1-t) * f( t / (1-t) = OuterSum: n=0 |--> +infinity { InnerSum: k=0 |-->n ( n : choose k) ( -1)^k / (2k + 1) } * t^n Then: Sum: k = 0 |--> n (n: choose k) (-1)^k/(2k+1) = (2n)!! / (2n + 1)!! Proving the above just refer to proving a binomial sum identity. We can see that: The Integral from 0 to infinity of Sin(x)/x dx is equal to: The Series: n=0 |--> +infinity {(2n)!!/(2n+1)!!}*(1/2)^n = PI/2. Forgive me if there's any typos in the math... "Y.T." isn't very friendly with their parsing of comments. Here's a link for the above Series: math.stackexchange.com/a/14116/405427

Love the « in the a world »

You know a guy is genius when he invents a new way to integrate!

I think this is a two-part trick method. First trick part comes from the need to “temperate” the integrand, which is swinging wildly. (Btw, we need to state, right off the bat, that a is positive.) This way we get a function, the temperated integrand, whose integral on [0,infinity) is finite. The second trick part is to use differentiation (under integral) wrt the parameter of the “temperator”.

I was upset about the dx until you fixed it! I found this derivation in high school, and loved it, and only now as an undergrad can I appreciate this technique's similarity to the Laplace or Fourier transform.

"Feynman Technique" is TH-cam's favorite moniker for "The method of integration by-parts". Just open up any elementary calculus book written before Feynman was born.