If M is also oriented, then it is possible to define a natural volume form from the metric tensor. In a positively oriented coordinate system (x,..., x) the volume form is represented as ω ω = | det g | d x 1 ∧ ∧ ⋯ ⋯ ∧ ∧ d x n where the dx are the coordinate differentials and ∧ denotes the exterior product in the algebra of differential forms. The volume form also gives a way to integrate functions on the manifold, and this geometric integral agrees with the integral obtained by the canonical Borel measure.