How do I prove that the wave function R_{10}(r) is normalized?

[karkas]

Homework Statement

Its simple, I've encountered this problem in Beiser's book and it doesn't seem right:

Prove that the function $$R_{10}(r) = \frac{2}{a_{0}^{3/2}}\cdot e^{-\frac{r}{a_0}}$$ is normalized.

Homework Equations

$$\int_{-\infty}^{\infty} |\psi|^2 dV = 1$$

The Attempt at a Solution

I figured it's simply just taking the integral
$$R_{10} (r)=\int^{\infty}_{0}( \frac{2}{a_{0}^{3/2}}\cdot e^{-\frac{r}{a_0}})^2dr = 1$$
but the result is not 1, it's $$2/a_0^2$$

 

[Simon Bridge]

Don't you need r²dr instead of just dr?
(volume integral, spherical-polar coords.)

 

[karkas]

Yes it appears that solves the problem, thanks!

 

[karkas]

I would enjoy a pointer as to where this comes from exactly, maybe a link?

edit: just standard triple integration in 3 coordinates?