# Thread: How to integrate this integral?

1. ## How to integrate this integral?

$\int_{0}^{\infty}x^2e^{-x^2/(2\theta^2)}dx$

2. Hello,

Note that this integral is half $\int_{\mathbb{R}} x^2 e^{-x^2/2\sigma^2} ~dx$

but then you can recognize $e^{-x^2/2\sigma^2}$ as nearly the pdf of a random variable Z following $N(0,\sigma^2)$

Try to find what $\sigma^2=E[Z^2]$ is, in terms of an integral and compute that integral.