The Gaussian Integral // Solved Using Polar Coordinates

The gaussian integral - integrating e^(-x^2) over all numbers, is an extremely important integral in probability, statistics, and many other fields. However, it is challenging to solve using elementary methods from single variable calculus. In this video we will see how we can convert it to multivariable calculus and then use tricks from multivariable calculus - in this case converting to polar coordinates - to solve this single variable integral. The crazy thing is that this integral ends up being in terms of pi, and if you didn't know about the polar trick you might wonder why pi shows up here at all! This proof is due to Poisson.

The previous video on double integration in polar: https://www.youtube.com/watch?v=U-13q74uvTo

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This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.

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Видео The Gaussian Integral // Solved Using Polar Coordinates канала Dr. Trefor Bazett