Main Question or Discussion Point
integral of e^(-x^2)dx?
Here's a nice Wikipedia link to show you the double integral. It's a page on the Gaussian Integral, which is the same integral as yours, but a definite one. It convertswhozum said:Usually done as a double integral with polar coordinates. I think its Fubini's Theorem.
I have not seen it myself, but I heard that it is quite long (a dozen pages, I heard)Watts said:Does there exist a proof that says that it is impossible to produce a closed anti derivative of f(x)=e^-x^2? I would like to see it if it does exist.
Well, there's an answer to that question, but it's kind of disapointing. By definition:Watts said:If it is impossible to generate an anti derivative through the use of elementary functions could some one please produce an anti derivative with non-elementary functions?
Yes, it is impossible. This is important enough that it's in just about every treatment I've seen on "integration in finite terms" (<-buzzwords for google), so there will be many options, such asWatts said:Does there exist a proof that says that it is impossible to produce a closed anti derivative of f(x)=e^-x^2? I would like to see it if it does exist.