Integral with a limit

Here I evaluate an integral with a limit, using the celebrated Dominated Convergence Theorem. Come and watch this video, this is pure mathematics at its finest!

[routemath]

The mighty Dominated Convergence Theorem strikes again, awesome! :-)

[insouciantFox]

When guessing, guess π.
When in doubt, Euler did it.

[arvindsrinivasan]

If you decide to take the “hard” route and integrate first, the integral gives
pi*n*(1-e^-(1/n))

[I integrated this using Residue Theorem and recognizing that the real part of (e^(i*x/n)-1)/(i*x/n) is equal to sin(x/n)/(x/n) ]

Taking the limit as it goes to infinity requires taking the limit of an indeterminate argument, but is quite easy to show it gives pi

[blightedcrowmain]

i like how he says ty for watching at the beggining

[LatestBinge]

Love your videos! I'm an 8th grader but thanks to you I start to understand and love complex math!

[RalphDratman]

I enjoy mathematics but this is one of those moments when I become very aware that I could never become a mathematician.
I did become an engineer (of computer-related hardware and software), but unofficially.
Now that I'm retired, I wonder how I ever managed to do any of that!

[umerfarooq]

Great video informative, interesting and nonetheless entertaining especially the "some kind of people"

[danielaorozco]

feels like magic :0 thanks a lot doctor!

[AnkitSharma-efmd]

Dr. Peyam is high on mathematics.
I loved the approach.
Coolest professor I ever have seen.
Wished you were my post graduate professor..
😁😁😁😁😁

[TheAustrianAnimations]

This video got randomly recommended to me. Nice, I've learned something new.

[tejpalsinghantal]

Mandatory comment to help with the algorithm

[joelschwed]

There is no limit to your wisdom good sir...

[shivaudaiyar]

Thanks for such a great content with love from India

[rounaksinha]

Happy mathematics day
Perfect integral for Mathematics day

[adam_elm_]

im happy when I get a notif of a new video!

[comingshoon]

gracias Doctor Peyam... ahora ya sabemos que los límites pueden ingresar dentro de una integral sin problemas jejej ... saludos desde 🇨🇱🇨🇱

[Chariotuber]

great video as always dr peyam! this really brings me back to when I took a mathematical physics class, which basically ended up being a class on functional analysis. good times lol

[IoT_]

7:26 I'm an engineer and I don't understand why you didn't allow to put equal sign between sine function and x on your math channel 🌝

[jiteshsingh]

Make video on value of evolution of 'e'

[ucr]

If I were a math professor like you, I would put this problem in a Calculus 2 Final exam or an AP Calculus BC exam. Heck, it might even be an extra credit problem. Why? For starters, because you would have to probably use L'Hospital's rule and you definitely need your trigonometry skills to solve this problem. Second of all, this problem's solution can be messy like a chili cheeseburger and takes a lot of time to solve (at least 9-10 minutes). A typical Calculus 2 problem takes like 5-7 minutes to solve. Third and finally, this is one of the hardest Calculus 2 problems that I have seen in my life.