This is the first time in my life I have ever heard the phrase "reverse cowgirl" applied to mathematics and it's got me giggling. 😂 Physics: "for simplicity in this example we will assume a spherical reverse cowgirl in a frictionless vacuum..."
thanks a tonnn !!! i can finally understand this integral because the feynmann technique is fantastic. i can literally understand the gaussian integral at 17 !! THANKS A TONNN
Another way is, simply do substitution x^2 = t, then use Feynmann technique within this use the Gamma function and then the Laplace transformation porperty, L [f(t)/t] = int{s to inf} L(S) ds.
Cool! Really cool! I do not know how many ways to solve the Gaussian integral I have seen so far, including contour integration, and I am still fascinated and excited by yet another approach... Yes, maybe squaring and using polar coordinates is the easiest and most popular way but using various other approaches is a good massage for the brain... Besides, it keeps your vigilance to be able to see similar possibilities in solving other integrals.
I couldnt even do simple equations in math yet i‘m here watching this and literally understanding zero. This stuff gives me ptsd from highschool times.
Paul Nahin's 'Inside Interesting Integrals' is an entertaining book. He has a Chapter on Feynman's technique and another on contour integration. That is only 2 of the 9 chapters. There are some mind blowing problems in there about realistic problems from math and physics.
Ah yes the interchange of limits....you're right....although the integral's convergence is trivial given its form it would've been better to mention this to justify taking the limit inside the integral operator
I evaluated the fresnel integrals the same way so I applied it here. I got the fresnel integral approach from flammy but he messed up near the end with the complex exponential so I just improved on it.
@@maths_505 i'll be honest here, im just watching these vids for fun cuz my love's not with me and im kinda lonely and missing her haha... math's just awesome! i haven't studied calculus in that depth but watching you makes me realise there's so much i need to learn, thanks ❤️
Your thoughts on the current controlled extraterrestrial reality disclosure process and related US GOV cover-up? When the nervous contagious giggling subsides, how will our civilization adapt to this publicly known reality? What might be some of the potential implications of disclosure of this reality? New energy sources perhaps? Religions? History? Do we really want to know the full truth?
Gamma function approach is the simplest one....if anyone complains about the Γ(1/2) thing, I would direct them to the reflection formula for the gamma function.
@@maths_505 I agree. However, the polar coordinate approach is more elementary: we learned how to calculate the Gaussian before we evn heard about the gamma...
NOT THE REVERSE COWGIRL FOR INTEGRALS NOOOOO
😂😂😂
This is the first time in my life I have ever heard the phrase "reverse cowgirl" applied to mathematics and it's got me giggling. 😂
Physics: "for simplicity in this example we will assume a spherical reverse cowgirl in a frictionless vacuum..."
Unexpected but welcomed.
No because I told my mom I would keep my youtube PG while watching my brothers and she literally walked in when it said reverse cowgirl
""Physics is like sex. Sure, it may give practical results. But that's not why we do it."
- Dick Feynman, who probably enjoyed cowgirl
In my opinion, the smoothest evaluation of the Gauss integral is to take its aquare, write it as a double integral, and use polar coordinates.
Yeah I saw some paper and they said... This is an elementary approach so much more tricky to find. More advanced techniques make it way more trivial.
thanks a tonnn !!! i can finally understand this integral because the feynmann technique is fantastic. i can literally understand the gaussian integral at 17 !! THANKS A TONNN
Succesfully understood the whole concept...
What a truly beautiful way to evaluate the Gaussian integral! Your work shall not be underappreciated.
At some point it looked like Laplace's approach but it is actually a great approach.
But the easiest way is squaring and using polar coordinates
No fancy uses of Gamma function properties, a clean approach. Nice!
Another awesome integral! Can't stop watching these!
😂😂😂 I was hooked at reverse cowgirl trick for integration
If only youtube would allow me to use the corresponding thumbnail
@@maths_505 Technically you could, you'd just have to use a different platform.
Ah yes....maths 505 on the hub😂
I did watch the video with on hand….the other hand was had a pencil in it following along
Had us in the first half not gonna lie
Doesn't 2:00 follow from the fundamental theorem of calculus, no differentiation under the integral required?
Indeed it does but the Leibniz rule provides a nice insight into its mechanism
You’re right, we should just use the fundamental theorem of calculus at that step.
Another way is, simply do substitution x^2 = t, then use Feynmann technique within this use the Gamma function and then the Laplace transformation porperty, L [f(t)/t] = int{s to inf} L(S) ds.
"A crazy approach" That alone tells you that it's gonna work.
Cool! Really cool! I do not know how many ways to solve the Gaussian integral I have seen so far, including contour integration, and I am still fascinated and excited by yet another approach... Yes, maybe squaring and using polar coordinates is the easiest and most popular way but using various other approaches is a good massage for the brain... Besides, it keeps your vigilance to be able to see similar possibilities in solving other integrals.
I would define the square of the integral to be J(t) not I(t), namely because I is defined as being the integral from zero to infinity.
I couldnt even do simple equations in math yet i‘m here watching this and literally understanding zero. This stuff gives me ptsd from highschool times.
That was very, very clever. Especially the substitution part....
This is a really cool way to do it besides switching to polar. Nice!
I watched the video and started crying after 40 seconds
Thanks, this is one of my favourite videos on all the platform, never really understood polar cordinates :p
Can anyone suggest me a book to start with feynmanns integrals???
Paul Nahin's 'Inside Interesting Integrals' is an entertaining book. He has a Chapter on Feynman's technique and another on contour integration. That is only 2 of the 9 chapters. There are some mind blowing problems in there about realistic problems from math and physics.
@@robertbachman9521Thank you very much, this will be so helpful for physics.
I didn't quite understand the change of variable in 3:31 can someone explain? thank u
We can use the gamma function and it will be in the end gamm(1/2)= √π
When taking the derivative why you do these with the limits? Is there a general rule?
The Leibniz rule
@@maths_505 okay and why d(0)=0?, how do you evaluate if you have a number
Which app are you using to annotate
at 0:54 why its square ? thank you sir.
Watch the rest of the video
It'll become clear
Very nice! Nitpicking, you could have explained why the limit can be taken inside the integral in the final step.
Ah yes the interchange of limits....you're right....although the integral's convergence is trivial given its form it would've been better to mention this to justify taking the limit inside the integral operator
bro just pulled a reverse feynman technique, never seen a partial derivative be taken out of the integral
wtf did I just watch lmao
The reverse cowgirl formulation of calculus
What application is he using to solve this integral?
I'm lost after 2:14...
how did u come up with the I(t) and then square it lol
I evaluated the fresnel integrals the same way so I applied it here. I got the fresnel integral approach from flammy but he messed up near the end with the complex exponential so I just improved on it.
@@maths_505 you're amazing man! no words only respect :)
@@maths_505 i'll be honest here, im just watching these vids for fun cuz my love's not with me and im kinda lonely and missing her haha... math's just awesome! i haven't studied calculus in that depth but watching you makes me realise there's so much i need to learn, thanks ❤️
excellent thumbnail choice
I have you to thank for it
@@maths_505 no problem :)
How can I suggest you a problem? Mail?
It's in the about section of the page
Thanks a lot for this cool solution👌
Well gamma function is op
Agreed
That's a cool trick
ahh... a classic problem solved in a classic way, you should try with contour integration next.
0:47 THIS IS NOT CLASSIC! THIS NOT CLASSIC AT ALL!
What else do you expect from the reverse cowgirl formulation of the gaussian integral 😂
You should check out qncubed3's video on the gaussian. It's pretty cool
@@maths_505 oh yeah I did, just wanted to see it from my fav youtuber, thought you might have a cool approach (his was also extrememly cool)
REVERSE WHAT?
Awesome!!!!
Ramanujan solved like this by square root he used beta function
Lovely!
Root pi
U r Monster
Seems to be overkill of this problem
Why I am not smart like you
I'm not smart....just persistent...so you can do it if I can
I love maths
Your thoughts on the current controlled extraterrestrial reality disclosure process and related US GOV cover-up?
When the nervous contagious giggling subsides,
how will our civilization adapt to this publicly known reality?
What might be some of the potential implications of disclosure of this reality? New energy sources perhaps? Religions? History?
Do we really want to know the full truth?
Why complicate things? It's useless! The polar coordinates method is still the best!
Gamma function approach is the simplest one....if anyone complains about the Γ(1/2) thing, I would direct them to the reflection formula for the gamma function.
@@maths_505 I agree. However, the polar coordinate approach is more elementary: we learned how to calculate the Gaussian before we evn heard about the gamma...