how Laplace solved the Gaussian integral

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Learn more calculus from Brilliant: 👉 https://brilliant.org/blackpenredpen/ (20% off with this link!) This is actually Laplace's method to evaluate the Gaussian integral, namely the integral of e^(-x^2) from -inf to inf. https://en.wikipedia.org/wiki/Gaussian_integral I believe this is a great method because calculus 2 students, with the knowledge of improper integrals and the willingness to see a double integral for the first time, should be able to understand. I will do it the classic way in my new 100 integrals video! Subscribe to @blackpenredpen so you don't miss it! Here's how to "integrate" e^(-x^2) with the error function: https://youtu.be/jkytxdedxhU 0:00 100 integrals part 2 coming soon 1:10 integral of e^(-x^2) from -inf to inf without using polar coordinates. 14:06 check out Brilliant! 🛍 Shop math t-shirts & hoodies: http://bit.ly/bprpmerch 10% off with the code "WELCOME10" ---------------------------------------- ***Thanks to ALL my lovely patrons for supporting my channel and believing in what I do*** AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff Julian Moik Hiu Fung Lam Ronald Bryant Jan Řehák Robert Toltowicz Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva ---------------------------------------- 💪 If you would also like to support this channel and have your name in the video description, then you could become my patron here https://www.patreon.com/blackpenredpen