Let \( f \) be an integrable radial function in \( \mathbb{R}^d \). Then
\[ \int_{\mathbb{R}^d} f(|x|) \, dx = \omega_{d-1} \int_0^\infty f(r) \, r^{d-1} \, dr, \]where \( \omega_{d-1} \) denotes the surface area of the \((d-1)\)-sphere of radius 1.