This problem and its evaluation could do any elite school integration Bee proud. Great to the see the Gamma function and the Beta Function pop up. Lovely solution development.
i wonder if there's some generalization for this improper integral for any power n in the integrand 1/(x^n + 1) or if there may even be a generalized antiderivative
The final answer can also be written as (pi/2024)*csc(pi/2024).
nice! Yep flip the sin over and there it is
Very fun exploration near the end!
Thanks! Yes i really liked that part of this problem :)
That ended up being a very interesting and fun problem.
thanks Mike! Worked out much nicer than what I expected originally :)
This problem and its evaluation could do any elite school integration Bee proud. Great to the see the Gamma function and the Beta Function pop up. Lovely solution development.
Thanks Mohan! Yes really liked this one and the fact that we get both an exact solution and a nice estimate. 👍
The approximation will improve every year!
yes its quite true! 😁
Bro Im straight laughing but this is great!
Thanks!
imagine the question just asked for 3dp lol
great video btw
Thanks!
i wonder if there's some generalization for this improper integral for any power n in the integrand 1/(x^n + 1)
or if there may even be a generalized antiderivative
there most definitely is, you can use the residue theorem to do it
Yes the formula is pi/ (a sin pi/a ). For a > 1
Yeah. I remember watching a Dr. Payam video on this generalization. Cool stuff!
The final answer can also be written as (pi/2024)*csc(pi/2024).
Michael Penn got a video on it, he generalized it.Check it out