G3. Integral Gaussiana: Demostración usando derivación bajo signo integral (Truco de Feynman)

▼ IMPORTANT ▼ In this video we will see another proof of the Gaussian integral, which is equal to the square root of pi, in this case using the fundamental theorem of the TFC calculus and derivation under integral sign (Leibniz's rule or Feynman's favorite trick). First we define a function of t, in terms of the integral of the exponential, and then we derive using power derivative rule, chain rule, and fundamental theorem of calculus, then we make a change of variable, again we apply TFC, we exchange derivative with integral, we integrate both sides to remove the derivatives, we calculate constant of integration by calculating the value of the function at zero, and finally we calculate the limit at infinity to obtain the value of the desired integral, all step by step. #Gauss #Integral #Feynman ---------- ** IMPORTANT LINKS ** Special integrals:    • Integrales interesantes   Integral course:    • Curso Completo de Integrales - Cálculo Int...   Special Videos:    • Members-only videos   Mathematics Review Course (Pre-University)    • Curso de Repaso de Matemáticas   ---------- ** SEE ALL MY COURSES HERE **    / arquimedes1075   ---------- ** BIBLIOGRAPHY ** Inside interesting integrals, Paul J. Nahin Calculus of a variable, James Stewart Calculus, M. Spivak Simplified Mathematics, by Conamat ---------- ** DONATIONS ** Paypal: https://www.paypal.com/cgi-bin/webscr... Channel memberships:    / @matefacilyt   Patreon:   / matefacil   ---------- ** MY OTHER CHANNELS AND SOCIAL NETWORKS ** Physics Channel:    / @matefacilfisica   Videogame Channel:    / @matefacily   Twitch:   / matefacil   MateFacil App: https://educup.io/apps/matefacil Facebook (Page):   / arquimedes1075   Twitter: @Matefacilx Instagram: @Matefacilx Discord:   / discord   ---------- #Matefacil #Matematicas #Math #tutorial #tutor #tutoriales #profesor ----