Uploaded October 2024 | Updated September 2026, 2 weeks ago
Here's a non-real way of solving Fresnel's integrals: the integral of sin(x^2) and cos(x^2) from -inf to inf. We will need to use the Gaussian integral, which is the integral of e^(-x^2) from -inf to inf and the result is equal to sqrt(pi). However, we will also need to use the imaginary unit i, but I am not sure...
This is how Laplace solved the Gaussian Integral: youtu.be/tCPQSobqFh4?si=SJRTU1qypNikY_E3
----------------------------------------
Big thanks to my Patrons for the full-marathon support!
Ben D, Grant S, Mark M, Phillippe S. Michael Z, Jan P. Devun C. Stefan C. Ethan BW Didion S. NN Minkyu Y Brandon F Levon M shortsleeve Jack P Gabriel G David H Mateo F Emma M Kan L Yeeted C.
πͺ Support this channel and get my math notes by becoming a patron: patreon.com/blackpenredpen
π Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
----------------------------------------
#blackpenredpen #math #calculus #apcalculus
Here's a non-real way of solving Fresnel's integrals: the integral of sin(x^2) and cos(x^2) from -inf to inf. We will need to use the Gaussian integral, which is the integral of e^(-x^2) from -inf to inf and the result is equal to sqrt(pi). However, we will also need to use the imaginary unit i, but I am not sure...
This is how Laplace solved the Gaussian Integral: youtu.be/tCPQSobqFh4?si=SJRTU1qypNikY_E3
----------------------------------------
Big thanks to my Patrons for the full-marathon support!
Ben D, Grant S, Mark M, Phillippe S. Michael Z, Jan P. Devun C. Stefan C. Ethan BW Didion S. NN Minkyu Y Brandon F Levon M shortsleeve Jack P Gabriel G David H Mateo F Emma M Kan L Yeeted C.
πͺ Support this channel and get my math notes by becoming a patron: patreon.com/blackpenredpen
π Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
----------------------------------------
#blackpenredpen #math #calculus #apcalculus
