Here's another video on evaluating the gaussian integral using the Leibniz rule; the difference here is this one's much more extravagant and something you'd expect from Mr. Feynman
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..."
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.
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.
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
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.
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 ❤️
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...
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?
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.
Another awesome integral! Can't stop watching these!
What a truly beautiful way to evaluate the Gaussian integral! Your work shall not be underappreciated.
😂😂😂 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
"A crazy approach" That alone tells you that it's gonna work.
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!
Thanks, this is one of my favourite videos on all the platform, never really understood polar cordinates :p
That was very, very clever. Especially the substitution part....
This is a really cool way to do it besides switching to polar. Nice!
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.
Thanks a lot for this cool solution👌
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.
Lovely!
We can use the gamma function and it will be in the end gamm(1/2)= √π
That's a cool trick
I watched the video and started crying after 40 seconds
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 didn't quite understand the change of variable in 3:31 can someone explain? thank u
excellent thumbnail choice
I have you to thank for it
@@maths_505 no problem :)
"reverse cowgirl for integration" ... subbed!
What application is he using to solve this integral?
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
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.
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
U r Monster
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.
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
at 0:54 why its square ? thank you sir.
Watch the rest of the video
It'll become clear
Oh no, not this pic of Feynman! 🤣🤣🤣
Had to this time 🤣
Well gamma function is op
Agreed
How can I suggest you a problem? Mail?
It's in the about section of the page
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 ❤️
Root pi
I love maths
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
Ramanujan solved like this by square root he used beta function
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)
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...
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?