Evalutate

$\displaystyle \int_{0}^{\infty}\frac{x^{2}}{\theta^{2}}e^{\frac{-x^{2}}{2\theta^{2}}}dx$.

I started by letting

$\displaystyle u=x^{2}\Rightarrow\\du=2x$

and $\displaystyle dv=e^{\frac{-x^{2}}{2\theta^{2}}}\Rightarrow\\$?

I believe I need to use polar coordinates, but I not sure how. Any help would be greatly appreciated.

Thank you