anonymous 5 years ago I feel like asking a question: how do you prove the integral of e^(-pi * x^2) from -infinity to infinity = 1?

1. amistre64

can we do a series on it?

2. amistre64

the ^(x^2) has me concerned

3. anonymous

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

4. anonymous

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