1
$\begingroup$

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

At lunch with a math friend years ago, he showed me an integral whose solution was, he said, so beautiful that it compelled him to become a professional mathematician. I scribbled the integral down on a napkin, but for the life of me I cannot remember the trick he found so compelling.

And these things are hard to Google...

$$ \int_{-\infty}^{\infty} e^{-x^2} dx $$

  • 0
    You can search maths in Latex [here](http://www.latexsearch.com/)2011-04-26
  • 0
    http://en.wikipedia.org/wiki/Gaussian_integral ; standard method is to compute the integral over the entire plane of $e^{-(x^2+y^2)}$ using polar coordinates, and then show that it equals the square of the integral you want.2011-04-26
  • 1
    Duplicate of http://math.stackexchange.com/questions/34767/int-infty-infty-e-x2-dx-with-complex-analysis and http://math.stackexchange.com/questions/34699/int-e-x2dx as well.2011-04-26
  • 0
    @Arturo & Ross: both links give the same proof... which is indeed quite slick. Cheers. (I would delete my question now, but it already has an answer, so this is disallowed.)2011-04-26

1 Answers 1