I “Solved” This Impossible Integral! 🧠

[@NumberNinjaDave]

What method did you use to approximate the integral?

[@blackman123official3]

No worries just define the error function as the solution to this integral 😂

[@NumberNinjaDave]

Hahahahaha

[@numbers93]

NGL I thought this was gonna be a 1 min prank vid and that he was gonna do exactly this 😄

[@NumberNinjaDave]

@@numbers93 lol

[@elibrahimi1169]

I used this method specifically to prove the 68.2% 95.4% and 99.7% of the population under a gaussian within 1,2 and 3 standard deviations respectively, although a taylor expansion solution isn't as nice as an elementary function since it's hard to do things like solve for a value or find the inverse function for example

[@NumberNinjaDave]

Oh that’s epic! I’ve never used this in a statistical application

[@elibrahimi1169]

@@NumberNinjaDave well when i had to i had no choice but to use it, and there we go

[@LordKazekage108]

how would you approximate the gaussian integral after this? i tried but im not sure

[@creepermandeo9116]

Yeah but this is, just as you said, an approximation. Besides you can evaluate the integral in the video from 0 to 1 with the same method as the gaussian integral because both are converging to a finite value over the limits of integration. You can take I as the integral from -1 to 1 of e^x² and since e^x² is an even function, your target integral will be I/2. Then you can use any of the methods used to solve the gaussian just with the limits being -1 to 1 instead of -infinity to infinity

[@NumberNinjaDave]

Very true, 🥷