= Volume element
{title2=$dV=|\det D\Phi|\,du_1\cdots du_n$}
{wiki}
Under a smooth locally invertible coordinate map $\Phi$ into Euclidean space, the positive <volume element> in a <multiple integral> is multiplied by the absolute <Jacobian determinant>. In three-dimensional <spherical coordinates>, $dV=r^2\sin\theta\,dr\,d\theta\,d\varphi$; in <cylindrical coordinates>, $dV=r\,dr\,d\theta\,dz$. The absolute value distinguishes positive integration measure from a signed orientation convention.
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