How could we prove the following equality?
$\int_{-\infty}^{+\infty}\mathrm{e}^{-x^2}\mathrm{d}x=\sqrt{\pi}$
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see here https://math.stackexchange.com/questions/188241/how-to-prove-int-0-infty-e-x2-dx-frac-sqrt-pi2-without-changi – Dr. Sonnhard Graubner Apr 24 '17 at 13:28
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https://math.stackexchange.com/questions/9286/proving-int-0-infty-mathrme-x2-dx-dfrac-sqrt-pi2 – wythagoras Apr 24 '17 at 13:28
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[https://en.wikipedia.org/wiki/Gaussian_integral] seems to have some opinions – Kitter Catter Apr 24 '17 at 13:29
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Hint (you'll find answers everywhere): $$ I=\int_{-\infty}^\infty e^{-x^2}\mathrm dx\implies I^2=\int_{-\infty}^\infty e^{-x^2}\mathrm dx\int_{-\infty}^\infty e^{-y^2}\mathrm dy $$
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