Solution

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{c}
{title2=$\int_{-\infty}^{\infty}e^{-x^2}\,dx=\sqrt\pi$}
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The Gaussian integral is
$$
\int_{-\infty}^{\infty}e^{-ax^2}\,dx=\sqrt{\frac\pi a},
\qquad a>0.
$$
Squaring the integral and changing to polar coordinates proves the formula.


Gaussian integral

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