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

How does one integrate $\int e^{-x^2}\,dx$? I read somewhere to use polar coordinates.

How is this done? What is the easiest way?

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    As an indefinite integral, this is not expressible by elementary functions. I guess you mean a definite integral?2011-04-23
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    This is an interesting integral. There is an expository paper by K Conrad dealing with this.2016-07-02
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    One of most elementary ways to prove it is using limits and arctangent : http://math.stackexchange.com/questions/9286/proving-int-0-infty-mathrme-x2-dx-dfrac-sqrt-pi2/1759809#1759809 Side note : On the same page are other solutions as well so check them out :)2016-07-15

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