Cylindrical volume element
= Cylindrical volume element
{title2=$dV=r\,dr\,d\phi\,dz$}
For $x=r\cos\phi$, $y=r\sin\phi$ and unchanged $z$, the <Jacobian determinant> of Cartesian coordinates with respect to <cylindrical coordinates> is $r$. Hence a <volume integral> acquires the displayed factor for $r\geq0$. The inverse determinant is $1/r$ where $r>0$; the axis is a coordinate degeneracy.