Integrate e^(-x^2) using a double integral, Multivariable Calculus
Автор: Dr. Bevin Maultsby
Загружено: 2024-09-02
Просмотров: 1039
Описание:
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.
#Mathematics #Calculus #Integrals #MathTutorial #MultivariableCalculus #MathEducation #MathTechniques #PolarCoordinates #AdvancedCalculus #calculus3 #iitjam
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