Question

I feel like asking a question:
how do you prove the integral of e^(-pi * x^2) from -infinity to infinity = 1?

Answer 1

can we do a series on it?

Answer 2

the ^(x^2) has me concerned

Answer 3

This is a very difficult question and you need to use the theory of multivariable calculus to solve it. See my answer to this question here: http://openstudy.com/study?F5769949656131Z2X2S=_#/updates/4f13da1ce4b0a4c24f58da32

Answer 4

Just perform the initial u-substitution \[u=x\sqrt{\pi}\] and the two problems will be exactly the same.