@@cougar1861 I thought about something like that, or maybe the distribution of them in the time, but we have to few data for that. We could rather do some qualitative studies, like, for instance, the time of the first occurrence or the second one. For instance I think that the first occurrence of the "ok, cool" comes (now) within the first 5 seconds, may be less, whereas for the second one, it's a bit more random. Also, we can say that they occurs after an important information, such as an important result or an abstract of some strategy. A very interesting topic, isn't it?
The way that immediately came to my mind is to notice that the integrand is an even function, so you can expand the integration from negative to positive infinity. Following that, at 4:23 you're left with what is just the inverse Fourier transform of e^-|t| (barring some constants of course) evaluated at k. You should totally introduce the Fourier transform to the toolbox in your videos, electrical engineers love it for a reason.
hey i just want to know if u use a trick i don't understand or smth but on wolframe your integrale from 0 to inf of cos(kx)/1+x^2 = pi/2e^k , i have personnaly solve it using contour integration and found the same resulte so ig it's the good resulte but something seem wrong.. may wolfram just wrong ?
Could u pleaseee explain to me why can we make the "Re()"real part outside of the integral and why can we use it again whenver we want to like shown at 4:40
I wish latex was integrated here to make the explanations alot easier but unfortunately I don't think RUclips plans to make the platform more math friendly. So I'm just linking a math stackexchange post here: math.stackexchange.com/questions/3817007/why-can-we-take-out-the-real-part-operator-from-under-the-integral
Proud to say I was able to solve this on my own before watching the video. You've taught us well Mr 505
Hi,
"ok, cool" : 1:33 , 2:49 , 3:53 , 6:27 ,
"terribly sorry about that" : 1:47 , 2:55 , 4:05 .
Are there any records for number of each 1) "OK, cool" and 2) "terribly sorry about that" ... per minute of video?
@@cougar1861 I thought about something like that, or maybe the distribution of them in the time, but we have to few data for that.
We could rather do some qualitative studies, like, for instance, the time of the first occurrence or the second one.
For instance I think that the first occurrence of the "ok, cool" comes (now) within the first 5 seconds, may be less, whereas for the second one, it's a bit more random.
Also, we can say that they occurs after an important information, such as an important result or an abstract of some strategy.
A very interesting topic, isn't it?
@CM63_France indeed it is
The way that immediately came to my mind is to notice that the integrand is an even function, so you can expand the integration from negative to positive infinity. Following that, at 4:23 you're left with what is just the inverse Fourier transform of e^-|t| (barring some constants of course) evaluated at k.
You should totally introduce the Fourier transform to the toolbox in your videos, electrical engineers love it for a reason.
Great solution. I laughed to myself when the significance of the final infinite series dawned on me.
Truly mesmerizing! Stunning result as well
at 6:09 you made a mistake on the integral from 0 to infty of cos(kx)/(1+x^2) the correct answer is pi/(2 e^k)
Exactly ,your right it's an error
You always pick the coolest integrals 😊
Very integral!
Much mesmerizing!
And 8 minutes ago??
You could use residue theorem right away so you dont have to do series expansion
Been there
Done that
Link in description
Very cool. Thank you.
I think this is off by a factor of 2. pi e^(e^-1) / 2. 6:00 result of that integral is pi/2/e^k.
Fantastic
Shouldn’t it all be over 2 ?
Indeed
Indeed x 2 which should cancel out the factor of 1/2 thereby justifying my result (terribly sorry about that)
Where’s the extra x2 coming from. As far as I can tell the final answer should be pi/2 e^1/e no?
Wow, that's very cool 😎
Hi Kamal,
You make use of the Dominating Convergence Theorem quite a bit. Have you considered doing a video proving this theorem?
Just a thought
please don’t ruin the fun with analysis 🙏
hey i just want to know if u use a trick i don't understand or smth but on wolframe your integrale from 0 to inf of cos(kx)/1+x^2 = pi/2e^k , i have personnaly solve it using contour integration and found the same resulte so ig it's the good resulte but something seem wrong.. may wolfram just wrong ?
Could u pleaseee explain to me why can we make the "Re()"real part outside of the integral and why can we use it again whenver we want to like shown at 4:40
I wish latex was integrated here to make the explanations alot easier but unfortunately I don't think RUclips plans to make the platform more math friendly. So I'm just linking a math stackexchange post here:
math.stackexchange.com/questions/3817007/why-can-we-take-out-the-real-part-operator-from-under-the-integral
@@maths_505 Thank You soooo much for your time dudde , Hope u solve hatder integrals and get much more gym gainzz
@@ryan_journey thanks mate
We can solve this using the fact that (e^cosx)cos(sinx)= sum to infinity of cosnx/n!
Ho-leee cow
Yeah
That's what I felt as well!
Breathtaking
hey are you indian ?
Legends know this is a re-upload
It's not a re-upload.....I previously solved it using contour integration.
@@maths_505 Oh my bad