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Proving $\int_{0}^{+\infty} e^{-x^2} dx = \frac{\sqrt \pi}{2}$

My calculus is a bit rusty, how should I solve this in order to calculate the solution?

$\int^{\infty}_{-\infty}e^{-x^{2}}dx=\sqrt{\pi}$

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marked as duplicate by Pedro Tamaroff, Alex Becker, David Mitra, William, DonAntonio Sep 14 '12 at 3:18

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

    
This is surely a duplicate. I'll see if I can find a previous version. –  Alex Becker Sep 13 '12 at 23:32
    
Thank you, I didn't know how to find the same formula –  John Smith Sep 13 '12 at 23:32

1 Answer 1

up vote 0 down vote accepted

if $I=\int_{-\infty}^{\infty}e^{-x^2}$ then $$I^2=\int\int e^{-(x^2+y^2)}dxdy=\int\int re^{-r^2}drd\theta=\pi$$

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