Solving the Gaussian Integral the cool way

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Check out MAPLE LEARN ►www.maplesoft.com/products/le.... Try out the limited trial version of Maple Learn
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My video on the "normal" way to solve the Gaussian Integral using a double integral in polar coordinates ► • The Gaussian Integral ...
In this video we're going to see a different trick to be able to solve the Gaussian Integral utilizing Feynman's trick of introducing a parameter.
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Опубликовано:

6 июл 2024

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Комментарии : 72

@bryangough6424 Год назад

Hello Dr. Trefor! I am an undergraduate student who loves your videos a lot. I have been struggling in my current major and really not felt confident in my studies. I think your videos have helped convince me that my passion lies in mathematics instead of the subjects I have pursued so far. Thank you so much for your content!

@DrTrefor Год назад

That's so kind of you to say, good luck!

@grahaml6072 Год назад

Wish I had RU-vid and channels like this when I was an undergraduate student. Unfortunately that was 30 years ago.

@ShanBojack Год назад

man i have a similar story

@agutilinus2828 11 месяцев назад

@@DrTreforhi

@fordtimelord8673 11 месяцев назад

@@grahaml6072 Same here. These RU-vid professors that share their knowledge, intuition and joy of a subject or problem are an incalculable blessing to mankind.

@caryfitz Год назад

I really liked this. Feynman's technique has always been obscure to me. Your description was revelatory! Thank you very much!

@DrTrefor Год назад

Thank you! Isn't it cool?

@212ntruesdale 11 месяцев назад

Who in the world is brilliant enough to come up with this?! I feel really smart just being able to understand what’s happening! There’s clever, and then there’s CLEVER. Know your station!

@DrTrefor 11 месяцев назад

so clever!

@ajb16384 4 месяца назад

I have an extreme love for math and I just discovered this channel. This is an absolute goldmine. Thank you Dr. Trefor

@slavinojunepri7648 11 месяцев назад

Wonderful proof. Thanks for sharing.

@johnchessant3012 Год назад

Wow, up until today I only knew the polar coordinates way of solving the Gaussian integral!

@Valori_4 9 месяцев назад

Hello! I'm currently 12 year's old studying in 6th grade but I'm a very curious person in learning mathematics and physics so I chose you to teach to solve this infamous Gaussian Integral Hope when I get older I'll find a new invention like any other scientist's ❤ Thanks to you for your video's You got a new sub❤

@ryemiranda6800 9 месяцев назад

Same im 13 and in algebra 1

@Valori_4 9 месяцев назад

@@ryemiranda6800❤

@kasg8427 Месяц назад

I am 9 year old

@umairbutt1355 7 месяцев назад

This was my first proof of the gaussian that I came across and it blew my mind (I didn't study multi-variate calculus yet). Does anyone know the original author of this proof?

@user-cg7gd5pw5b 3 месяца назад

Thanks, I've done multiple exercises where they give the developed derivative and you have to climb back to the Gaussian integral, and was always wondering how people found this kind of expressions in the first place.

@foysalsahriar5608 11 месяцев назад

Hi, Really nice video! I was wondering if I can help you edit your videos and also make highly engaging shorts out of them.

@aweebthatlovesmath4220 Год назад

Nice video! it's always good to solve a problem in more then two ways. i mean all and all it's not the answers that make math interesting it's the way we do math!

@DrTrefor Год назад

Absolutely, and we often get stuck only knowing the "normal" way things are done

@monsterhunter8595 Год назад

Nice

@monke9865 Год назад

Interestingly there is another way to compute this integral using single variable calculus, with strong geometric flavor. Consider F(r)= int _{x^2+y^2

@AssemblyWizard Год назад

This is multivariable..

@marylinebentzinger7378 Год назад

Can somebody explain why we introduced y and why when we introduced the new variable y, we set the top border to one?

@DrTrefor Год назад

It's just a change of variables y=x/t. Specifically when x=t for the upper bound, in the new variable y=t/t=1. The point of this change of variables was to get the parameter t out of the limits of integration and into the integrand.

@marylinebentzinger7378 Год назад

@@DrTrefor thank you so much, it seems so easy right now, you must have a gift for maths

@MurshidIslam Год назад

Shouldn't it be −arctan 1 + arctan 0 + C at 7:26?

@balubaluhehe2002 Год назад

It should've been, because there was a negative sign at the front, but -0 or +0 didn't change the final result at all.

@DrTrefor Год назад

Oops, good catch. Yes irrelevant for the end result:)

@josafajunior5425 Год назад

7:25 That signal it's wrong? Don't changed because is zero, but should be +arctan(0)?

@EdoardoDAurelio Год назад

That Englishal it's wrong too lol

@tg0406 4 месяца назад

I remember solving this using power series and differential equations

@strikerstone 8 месяцев назад

Really fun if you understand imo

@airman122469 Год назад

Before the video started: “Feynman technique?” Video starts: Feynman technique.

@alebaldus9229 11 месяцев назад

Grazie.

@DrTrefor 11 месяцев назад

Thank you so much!

@user-rq6gd8yy2t Год назад

What A WAY😮😮😮😮

@andrewharrison8436 Год назад

50 years ago I felt that integration was a black art. If anything videos like this confirm it. Love the way that the annoying C that crops up in any integration turns out to be the part that carries the result from the doable integral to the unknown one. I will probably watch this again to see exactly when you hid the rabbit in the top hat.

@DrTrefor Год назад

Ha ya it really is tbh, so many cool tricks to learn

@ahmedyacine5661 11 месяцев назад

This guy here is so nice

@egor.okhterov Год назад

Why?

@joelchristophr3741 9 месяцев назад

Sir i dont understand one thing .. that is how did you assume that f(t) is a square of that integral initially?????

@umairbutt1355 7 месяцев назад

It's not an assumption. It's a definition for f(t). Now, the question of WHY such a function f(t) was defined in order to get to the gaussian is the really interesting question 😅😅

@joelchristophr3741 7 месяцев назад

yeah... i understood.. thankyou :) @@umairbutt1355

@MooImABunny Год назад

Gozeean integral. Hey look, it's Dr. Chreethaw, he's gonna us Mothimautecs

@samtux762 2 месяца назад

Neat approach. But I wouldn't dare to repeat it and would go for the classic switch to polar coordinates. But, I am not in math (was in chemistry), so this isnot my field.

@samtux762 2 месяца назад

Integrals arenot my jam and are not a part of my work. But I added your channel to my watch list. This "I will just use Feinman approach and square" came out of the blue. Brain massaging. Love it.

@sandorszabo2470 Год назад

Tricky solution! However it is not the "Feynman's trick". This method was known earlier. Only Feynman was the person who used a lot to simplify the calculation of many complicated integral.

@Sciensistbikon 6 дней назад

Feynman integral !?

@ViralShorts_2323 Год назад

What is the need of taking partial derivatives?

@DrTrefor Год назад

It's just a partial because the integrand is a function of both x and t

@ViralShorts_2323 Год назад

@@DrTrefor Dear Sir, don't we concern with 't' only?

@user-xo5th3cm5k 2 месяца назад

11 12 22 4..

@gnarlybonesful Год назад

disappointed you didn't prove the limit was 0 and instead justified it by looking at a graph!

@mariostelzner4530 Год назад

WHY BUST YOUR BRAIN TRYING TO REFIGURE OUT SOMETHING THAT'S ALREADY BEEN SOLVED. AHAHAHA AHAHAHA LOL

@Ben-rd3mg 3 месяца назад

Such an evil way to solve it

@avinashyadav8314 Год назад

No offence but Polar coordinates were much better 🫠

@DrTrefor Год назад

ha, I like both!

@grahaml6072 Год назад

1st

@monsterhunter8595 Год назад

Haha

@grahaml6072 Год назад

@@monsterhunter8595 I don’t know why people do that and post they first but this just happened to be the only time I have ever been first so I thought what hell I will look like an idiot like all the others 😀

@DrTrefor Год назад

ha, nice one!

@diezelvh4133 6 месяцев назад

So, if you're technically first, is every other comment under your first comment first also? ...

@billcook4768 Год назад

No, no, no. In order to truly be “cool”, you have to use Taylor series. It’s like a law or something. Then again, for the life of me I don’t see a Taylor expansion so maybe there is no official cool method :)

@DrTrefor Год назад

Taylor series is all good, but the question becomes for definite integrals what does that series sum to? We might get that it converges but harder to know in general if there is a nice answer for the sum