The Gaussian Integral is DESTROYED by Feynman’s Technique

In this video I demonstrate the method used to solve the Gaussian integral using Feynman’s integration technique, I was very excited to present this video as it combines 2 of the math world’s favourite internet concepts, the Gaussian integral and Feynman’s integration technique.

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Video Creator: Jago Hodges

[sergiogiudici]

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

[atmcollision]

When I heard Ballade 1 I thought I had another tab open, but it turns out that you have executed the amazing idea of allowing us to ascend even more than when we follow along with the maths...

[harley]

Seriously keep doing what you’re doing. The content is great. Your explanations are easy to follow and I thought it was a super fun video. I don’t mind the music at all. Everyone is being too pedantic either about the music or about the math but both are great and in combination even better. Keep at it! Loved this video.

[TheFinav]

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

[renesperb]

I find the calculation of this integral by using polar coordinates much more elegant. Debussy's Arabesque as music in the background is nice.

[plkrishh]

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

[MikelMath]

One thing I never liked about this integration technique is that it is not obvious how to choose the auxiliary function. So it is difficult to teach to students, as they would just have to guess at the auxiliary function (or memorize examples) and hope for the best! Feynman has written that he learned the method from a 1926 math book by Frederick Woods (Advanced Calculus: A Course Arranged with Special Reference to the Needs of Students of Applied Mathematics) that was given to him by his high school physics teacher. Perhaps there were enough examples in that text that Feynman knew a whole whack of sample integrals to solve with this method.

[victorsauvage]

Terrific -- Clearn and natural and benign and adult manner and tone -- This 'style' -- (which cannot be just 'put on' for the occasion -- It comes from being completely comfortable with one's subject matter) -- is so important for the simple quality of 'effective communication' -- i.e. necessary for 'communication', as such. Puts the pupil at ease -- but also enables complicated ideas to be easily absorbed by a beginning pupil -- whether the pupil is learning mathematics or the staff of a corporation or voters going into an election or the troops going into battle. (As David Hilbert said -- the leading research mathematician of the XX century, "You don't really understand a concept until you are able to explain it to the layman.")

[erickappel]

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

[yassimolaoc]

why is feynman zesty in all your video?

[mikezulu]

This is brilliant! However it probably takes nobody less than Feynman himself to come up with the idea of introducing 1 + x^2 into the equation.

[norliegh]

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?

[oxbmaths]

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.

[lindsaywaterman]

The Feynman Technique is actually the Leibnitz Method, ; it was invented by him during the time of Isaac Newton.

[ziggyw]

It would be much better if you turn that noise in the background off.

[hotelmasternm]

@18:31 some people use a and b and some people use s and t. Depends on whether the lower or upper limit is undefined

[samylahlou]

Nice video ! I really liked it ! But OMG what are these comments ?

Most math videos have music in the background and most of the time it’s louder than here. Do you guys write such comments on 3b1b videos ? If Chopin distracts you SO much, then you may be the problem, not the author of the video.

Concerning Feynman’s Technique, everyone knows that he didn’t invent it but that’s how we call it today. If you get so mad for someone calling this technique Feynman’s Trick, then be as mad if someone talks about the Pythagorean Theorem (which was known centuries before Pythagoras), get mad if someone talks about Fourier Series or Fourier coefficients (Euler found them 30 years before Fourier), get mad if someone talks about Riemann sums (the concept was already well known and used since Leibniz but also by Cauchy who, before Riemann, defined the integral for continuous functions).

Again, concerning Feynman’s Trick, the goal is not to understand where the function f comes from, this is not a lecture where you need to be able to do the same on the exam, the goal is just to show another way of solving the integral. Everyone knows that the usual technique for this integral is easier. The goal is not to present an easier technique but simply another technique than the usual.

Again, thank you for the video, I really liked the explanations and you made every step very clear. Thank you !

[cakiral]

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

[ethanbartiromo]

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

[yevgeniygrechka]

I'll have to go through this is detail, but one thing is for sure, the polar coordinate method is far simpler for solving this particular integral.