Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §8.4 Probability and Calculus, #14 · Probability · Continuous distributions

Show by substitution that … \int_{-\infty}^{\infty} e^{-x^2/2\sigma^2} dx = \sqrt{2}\sigma \int_{-\infty}^{\infty} e^{-u^2}…

Show by substitution that
$\int_{- \infty}^{\infty} e^{- x^{2} /2 σ^{2}} d x = 2 σ \int_{- \infty}^{\infty} e^{- u^{2}} d u = 2 π σ .$

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §8.4 Probability and Calculus, #14

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