Math Help - Improper Integral

1. Improper Integral

Prove that $\int_{-\infty}^{\infty} dx\: e^{-i x^2} = \int_{-\infty}^{\infty} e^{-ix^2} dx$

2. Re: Improper Integral

Hey strammer.

There is no work to do: they are both the same integral.

Putting a dx on one side doesn't change the nature of the integral.

3. Re: Improper Integral

They apparently are not the same since d(xe^-ix^2) = e^-ix^2(1-2ix^2)dx

4. Re: Improper Integral

The post didn't have a bracket around the differential measure so I missed that.

If the function is differentiable, then d(g(x)) becomes g'(x)dx and you can integrate as per normal.