Question

Any novel approaches to this integral? I only know one way to do it\[\large\int_{-\infty}^{\infty}e^{-x^2}dx\]

Answer 1

which way do you know? i recall seeing a few...

Answer 2

Are you in college?

Answer 3

double integral in polar coordinates

Answer 4

while i was learning about differentiation under the integral, i did come across such a proof for it:
it's probably not the most intuitive one but i spose it is one nonetheless. :p

from http://www.math.uconn.edu/~kconrad/blurbs/analysis/diffunderint.pdf from p.4 - 5

Answer 5

great, I wasn't looking fot intuitive, I wanted novel :D
I know this is was a favorite method of feymnan's, so this should be a good read

Answer 6

usual method is to square the integral then use polar
not sure of any other method

Answer 7

yeah that's the only one I know, hence I want another

Answer 8

oh yes, i did see this item too, goes over a lot of different ways to look at it.
http://www.math.uconn.edu/~kconrad/blurbs/analysis/gaussianintegral.pdf

Answer 9

oh that's just what I was looking for. Thanks, Access

Answer 10

glad to help!
of course, last time i saw this i was infinitely confused on some of those. i might have to look at this again now! :)

Answer 11

yeah this is clearly something I'll have to read in-depth, but it's well worth it, i'm sure

Answer 12

that should keep you busy for the rest of the weekend