Hi, I was just working about retrieving the first integral by Feinman technic, a couple of hours ago. The one which is equal to pi^2/6 . If you try to solve the Basel problem starting from 1/(1-x)=1+x+x^2+x^3+... , by intregrating, then dividing by x, then integrating again, you come across this integral. "ok, cool" : 0:17 , 3:01 , 5:11 , 5:53 , "terribly sorry about that" : 1:56 , 6:06 , 8:56 .
I thought I was alone 10:09 , I CSNT do arithmetic. On my CALC AP exam, I started counting with my fingers on the no calculator portion that made me do arithmetic…
I got to admit that your approaches to compute integrals are pretty awesome on an academic level however I think if you brush up on and make note of theorems and axioms on when it is allowed to differentiate ,switch sum sign with improper integral sign because the way I learned ,they were crucial to start off calculating , and I am sorry if my critique wasn't instructive
Convergence of the integral function will suffice. You can show that using various tests like dominated convergence, Dirichlet's convergence test etc. I've solved alot of integrals using Feynman's trick and you can find all of them in the playlist. In alot of those videos, you'll find me explaining why the switch up of operators is justified. However I do skip over that often because (depending on the integral) I find it so trivial to the point that I just want to get on with the actual solution.
@@maths_505Bro u also got me for a second to type that on comment but some part of my brain told let's wait till the end and there we go U pulled a prank on us .😂
Basic arithmetic is the final boss of maths, don't worry we all struggle. I feel your pain.
Then accept pain and know pain those who don't know pain will never understand true peice
that 1/16 - 1/6 gave me nightmares, truly the hardest problem
When the pathetically weak side boss comes back as the invincible main boss at the end of the game:
Hi,
I was just working about retrieving the first integral by Feinman technic, a couple of hours ago. The one which is equal to pi^2/6 . If you try to solve the Basel problem starting from 1/(1-x)=1+x+x^2+x^3+... , by intregrating, then dividing by x, then integrating again, you come across this integral.
"ok, cool" : 0:17 , 3:01 , 5:11 , 5:53 ,
"terribly sorry about that" : 1:56 , 6:06 , 8:56 .
"one baller integral" Finally, an integral for us one-ballers
😂😂😂
From your thumbnail, I'm ready for some R-rated Math!
Great solution , thanks for work your hard work that you've done to make this video exist.
It's been months and I can't think of a clever LOTR reference that relates to this.
Very nice result. Thank you
Runner up best math video
I thought I was alone 10:09 , I CSNT do arithmetic. On my CALC AP exam, I started counting with my fingers on the no calculator portion that made me do arithmetic…
I used to be so good at it back in high school. Now it's my greatest weakness.
I know those videos don't tend to do too well, but I'd love to see you do some more physics at some point.
'Basic' arithemetic, yet everyone struggles with it. They say "Poisson is kept in small bottles." in this case, a 'basic' bottle.🤷♂
Magnificent
Arithmetic is hard. I just use Mathematica. However Euler was awesome at it, computing ζ(2n) up to (IIRC) n= 6 or 7 or so.
also you made an error at the very end and wrote ln²(2)/8 insteand of minus ln²(2)/8
Check again😂
@@maths_505 am I missing something ? I = I1 - I2 and I2 = -5π²/96 + ln²(2)/8
@tirterra1222 12:32
@@jkid1134 looks like I clicked out of the video too fast. That's on me :/
I got to admit that your approaches to compute integrals are pretty awesome on an academic level however I think if you brush up on and make note of theorems and axioms on when it is allowed to differentiate ,switch sum sign with improper integral sign because the way I learned ,they were crucial to start off calculating , and I am sorry if my critique wasn't instructive
Convergence of the integral function will suffice. You can show that using various tests like dominated convergence, Dirichlet's convergence test etc. I've solved alot of integrals using Feynman's trick and you can find all of them in the playlist. In alot of those videos, you'll find me explaining why the switch up of operators is justified. However I do skip over that often because (depending on the integral) I find it so trivial to the point that I just want to get on with the actual solution.
Nice video ! Can you please do more multivariable integrals :p
It feels like you're just leading me in circles...
ln(1-x)/x = 1/xΣxⁿ/n => Σ xⁿ/n²|x=1 => ζ(2)
You forgot the -1 for the log series expansion
First, at last
There willl be minus before (1/8) ln^2 (2) in final result..
@@rajivb9493 exactly what I got
@@maths_505Bro u also got me for a second to type that on comment but some part of my brain told let's wait till the end and there we go
U pulled a prank on us .😂
@@aravindakannank.s. 😂😂😂