Could you help me with this?

By considering the integral of $\displaystyle e^{-yx^2} $ over a suitable region of $\displaystyle \mathbb{R}^2 $, show that for $\displaystyle 0<a<b<\infty $,

$\displaystyle \int_{0}^{\infty} \frac{e^{-ax^2} - e^{-bx^2}}{x^2} dx = \sqrt{\pi} ( \sqrt{b} - \sqrt {a} ) $