On a "general" differentiable manifold (without additional structure), differential forms "cannot" be integrated over subsets of the manifold; this distinction is key to the distinction between differential forms, which are integrated over chains or oriented submanifolds, and measures, which are integrated over subsets. The simplest example is attempting to integrate the -form over the interval . Assuming the usual distance (and thus measure) on the real line, this integral is either or , depending on "orientation:" formula_73, while formula_74. By contrast, the integral of the "measure" on the interval is unambiguously (i.e. the integral of the constant function with respect to this measure is ). Similarly, under a change of coordinates a differential -form changes by the Jacobian determinant , while a measure changes by the "absolute value" of the Jacobian determinant, , which further reflects the issue of orientation. For example, under the map on the line, the differential form pulls back to ; orientation has reversed; while the Lebesgue measure, which here we denote , pulls back to ; it does not change.