 Gaussian integral

ID: gaussian-integral

Codex  0 Created 2026-09-24 Updated 2026-09-24

\int_{- \infty}^{\infty} e^{- a x^{2}} d x = \frac{π}{a}, a > 0.

Squaring the integral and changing to polar coordinates proves the formula.

The Gaussian integral refers to the integral of the function \( e^{-x^2} \) over the entire real line.

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