So much of "we're on the right track if it looks cool" comes from being able to recognize the patterns, which comes from practice with the patterns. (Also, I'm very sure the author is aware of many integrals where "it looks cool" takes you down the wrong rabbit holes.)
When can you swap the integral operator and the Re/Im operators? because it's not always the same result, I think I saw some examples for this with path integrals... By the way, your videos are amazing!
@@איתיבירנבוים oh yeah path integrals are a whole different ball park. For "regular" you'll come across like the ones on my channel, if it doesn't seem divergent, go for the switch up. The actual rigorous approach is dominated convergence.
Pretty epic but I'm tired of these answers always having π and e. Maybe you could try also some other interestingly enough integrals that don't follow these typical answerss? Please :D
I love this stuff but can you tell me - did you just pick all the tricks you wanted to use THEN come up with an integral that could be solved with them?
i have try the residue theorem on it by substitue e^ix = y, but i can't get the right result i don't know why i always got 2epi it like doing the integrale from 0 to 2pi, i don't understand why it's not working
Kamal, can you formulate the tools you use before you start solving ? It gives me an opportunity to attempt on my own first and see how I screwed up in spite of the tips😀😀
@@maths_505you changed the sin x in the numerator using Euler's formula such that you got 2 exponentials, one of them being e^ix. Was wondering until the end of the problem why you didn't do that to the denominator
*pi(e-1), as k sum started at 1 instead of 0.
*thankfully* you're mistaken, he just accidentally wrote a 1 instead of 0(trace back to the double sum)
Yeah, happens at 9:49
So much of "we're on the right track if it looks cool" comes from being able to recognize the patterns, which comes from practice with the patterns. (Also, I'm very sure the author is aware of many integrals where "it looks cool" takes you down the wrong rabbit holes.)
I'm making a video related to that concept tomorrow 😭
Math is just magic
I love watching these videos as they satisfy my math brain needs. Keep up the good work man 👍
Hi,
"ok, cool" : 2:16 , 6:06 , 7:30 , 8:05 ,
"terribly sorry about that" : 3:06 , 3:51 , 8:23 , 10:21 , 11:16 .
Beautiful Result thanks for making video
At 8:10, sin((2k+1)x)/sin(x) should have equaled 1 + 2 * sum_(n=1)^k{cos(2nx)}
I was about to comment this mistake as well
fortunately, the answer was still correct as the term ended up going to zero anyway once the bounds of integration were applied
Ah yes, pie, served warm and tasty like some oily maccaroni.
Me used f(z) = eᶻ / (z - 1)
Contour |z| = 1
And then find half residue.
Fantastic
There is an error in writing the Dirichelt kernel.But it never changes the result.
Very nice solution, but the result should equal to ((pi*e/2)-1). This is due to starting index variable k from 1. Thank you.
When can you swap the integral operator and the Re/Im operators? because it's not always the same result, I think I saw some examples for this with path integrals...
By the way, your videos are amazing!
@@איתיבירנבוים oh yeah path integrals are a whole different ball park. For "regular" you'll come across like the ones on my channel, if it doesn't seem divergent, go for the switch up. The actual rigorous approach is dominated convergence.
@@maths_505 Monotone convergence theorem fascinates me so much as it gets rid of complex situations while solving questions.
So, at the end, we still don't know if it's rational or irrational :P
Pretty epic but I'm tired of these answers always having π and e. Maybe you could try also some other interestingly enough integrals that don't follow these typical answerss? Please :D
I love this stuff but can you tell me - did you just pick all the tricks you wanted to use THEN come up with an integral that could be solved with them?
Nah I don't often do that
4:14 can you substitute sinx by the imaginary part of e^ix ?
Y- No. That's like having an additional imaginary part in the denominator and it wouldn't lead you anywhere.
Very interesting! I have to ask, where do all of these integrals come from?
This one's derived from the 2023 MIT integration bee semi finals. It was an antiderivative problem that I tweaked.
dirichlet kernel is crazy. also the "i" in your imaginary part looks like a 9 ngl
i have try the residue theorem on it by substitue e^ix = y, but i can't get the right result i don't know why i always got 2epi it like doing the integrale from 0 to 2pi, i don't understand why it's not working
Kamal, can you formulate the tools you use before you start solving ? It gives me an opportunity to attempt on my own first and see how I screwed up in spite of the tips😀😀
can you do this using contour integration? and can you also do z/e^z -1 using contour integration from 0 to infinity
Do you usually check your work before uploading it? 😂
Only the final result in Wolfram alpha 😭
Do you want to share geomtry problems?
I'll ask the community if they want to see geometry here too.
How did you write sin[2k+1]x /sinx=.........
Where can i find a proof?
@@mohamadshakarami4258 Wikipedia
Kept wondering why you didn't change the sin x in the denominator to e^-ix until the end
What da??
@@maths_505you changed the sin x in the numerator using Euler's formula such that you got 2 exponentials, one of them being e^ix. Was wondering until the end of the problem why you didn't do that to the denominator
@@robertsandy3794 it's cool happened to me once too 😂
You should do a video with only black or very dark ink 😂
Which app do you use?
@@PetroGhost2890 Samsung notes
OK, Cool! ;)
So the answers 9. ~Engineers 😊
Yes indeed