I “Solved” This Impossible Integral! 🧠

The integral of e^x^2 has no known elementary function solution, but in this calculus II video, we're going to challenge what a "solution" really means. While you can't use integration by parts or u substitution on this integral, we're going to get creative.

On your calculus BC exam and especially in the real world, sometimes you may have to approximate solutions when no "real" solution exists, and we'll do that here with a Taylor series centered at a=0. Theoretically, any function can be represented by this infinite series and for real world application, that may not be fully applicable at infinity. However, we'll demonstrate how even taking just a few of the series terms can give a real good approximation for the area under the curve! Hope you enjoy!

0:00 - Introduction
0:17 - No "Real" Solution
1:42 - Taylor Series Approximation
3:10 - Finding Coefficients (e^y)
4:29 - Finding Coefficients (e^x^2)
5:05 - Real World Application

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