# Problem with integral

1. Aug 22, 2009

### Petar Mali

What is idea for showing this?

$$\int\int\ldots\int dx_1 dx_2\ldots dx_n e^{-a x^\top A x}=\sqrt{\frac{\pi^n}{\det A}}$$

$$A$$ is symmetric matrix, and $$a$$ is constant!

2. Aug 22, 2009

### g_edgar

(1) when $A$ is replaced by $U^{-1}AU$, where [tex]U[/itex] is an orthogonal matrix, the integral is unchanged.

(2) do the case where $A$ is diagonal

(3) any connection between (1) and (2) ?