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The Gaussian integral

MediumCalculus~6m

Compute ∫−∞∞e−x2/2 dx\displaystyle\int_{-\infty}^{\infty} e^{-x^2/2}\,dx. (to 3 decimals)

Show hints (2)+
  1. Square the integral and switch to polar coordinates.
  2. ∫0∞e−r2/2r dr=1\int_0^\infty e^{-r^2/2}r\,dr = 1.

Answer

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2.5066 (± 0.01)

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Asked at: Jane Street, Two Sigma

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