A monster double integral from the romanian mathematical magazine
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- Опубликовано: 2 авг 2023
- The 2 log integrals designed to give you a scare before scooby the contour doo bee doo unmasked them as pi:
• A wonderful applicatio...
The second ever RMM integral I've solved here on the channel and the solution development was indeed epic!
That was mine problem
❣️Thank you❣️for sharing such✨👏 nice solution ✨👏
You mean you're the one who presented it to the RMM?
That is so awesome!!!
Feels like I'm talking to a celebrity 😂🥳!!!
A subscriber emailed me this integral asking if I could solve it.... nd I must say it's a beautiful integration problem with those 2 log integrals needing a video of their own where I had to use contour integration.
Thank you for creating such a beautiful monster integral
@@maths_505yes!!
@@maths_505🙏Thank you 🙏 ✨that's your sublimity ✨and 🙏thank you 🙏 for such❣️ lovely words ❣️, really it ✨made my day ✨
Finally an integral in which γ doesn’t suddenly disappear at the end, I always feel bad for my boy macaroni not being invited to the party every time
I feel the same whenever I see \gamma terms cancelling out of nowhere
Both of the integrals containing log(1+x^2) can be solved without contour integration. The first in particular is elementary.
it's actually quite nice! use feynman's trick on ln(1+sx^2)/x^2 and the first one is quite clear. when you tack on an extra ln x, you do the same steps until you eventually get to integrate 0 to inf ln(t)/(1+t^2) dt which is equal to 0 by the usual t = tan theta substitution
Excellent double integral 🔥
Something about Eastern Europe and math ❤️❤️❤️💯💯💯
Very smart solution. Thank you.
LOL forgot you fix x as a constant inside the first integral. extremely nice result my friend.
you cant write ln(xu) as ln(x) + ln(u) and then separate the integrals in 2 integrals since you don't even know if the new integrals are well defined.
it's like saying that the integral from 0 to infinity of 0 is the integral of x - x is the integral of x - the integral of -x, you have inf-inf
Amazing! Where can I learn more about the Gamma function's properties and the constant that popped up in the end?
Scattered all over the channel 😂
im romanian! yeah rmm is wild sometimes
I've got a few more in my notes that I'll upload soon
@maths_505 Be careful - RMM often publishes incorrect solutions. There was a good example of this on MSE recently where the published solution derivation was incorrect in the first line and the rest was thus garbage.
@@ngc-fo5te interesting. Thankfully I prefer coming up with my own solutions and then cross check the final answer with wolfram alpha.
@@ngc-fo5te funny thing is when I mess something up and retrace my steps I often realize that I've evaluated a new integral altogether 😂😂😂
And don't call me Shirley
Hot 🔥
beautiful
Thanks
Can you solve the integral of :
ln(sinx+cosx)/(cosx-sinx) dx
Hey, I'm a bit confused by your Fubini theorem (I assume it's not about measure theory, since you mentioned continuity). But isn't it the case that for double Rieman integrals continuity suffices only when the rectangle (rigeon of integration) is bounded?
It works for the case of improper integrals as well provided the integral converges
@maths_505 Just converges or absolutely converges? I haven't looked at those theorems in the case of Rieman integral for a while, but if absolutely converges, then it's merely Fubini theorem for product measure.
@@user-fh5rm2ef4n convergence works just fine
How would such an integral ever occur?
Hi math 505 can you suggest some books from where one can study Bsc mathematics?
I think that means calculus 1,2 and 3
Linear algebra and differential equations.
Try MIT OCW on RUclips.
thanks a ton
Noice
Thanks
asnwer=1 isit thank you
is it me or you've been developing a lisp
I use adobe podcast to filter out background noises and for some reason it messes up audio at some places to make it sound like I have a lisp. It's pretty annoying for me when I watch my own videos but atleast I'm rid of the background noises. If you've seen my old videos you'll notice lots of background noise and even though I've moved houses and it's pretty quiet in my room, the air conditioning introduces considerable background noise
@@maths_505 i underthtand, i thought you thuddenly developed a lithp and i thought it wath kinda funny