In this video, I demonstrate how to compute the integral of e^(-x^2) from negative infinity to infinity, a famous and elegant example in calculus. Since e^(-x^2) does not have an elementary antiderivative, we use a technique that involves squaring the integral and converting it into a double integral. By switching to polar coordinates, we simplify the expression and compute the integral over a quarter disk in the first quadrant. By evaluating this double integral in polar coordinates, we show that the original integral is equal to the square root of pi.
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