The exterior derivative itself applies in an arbitrary finite number of dimensions, and is a flexible and powerful tool with wide application in differential geometry, differential topology, and many areas in physics. Of note, although the above definition of the exterior derivative was defined with respect to local coordinates, it can be defined in an entirely coordinate-free manner, as an antiderivation of degree 1 on the exterior algebra of differential forms. The benefit of this more general approach is that it allows for a natural coordinate-free approach to integration on manifolds. It also allows for a natural generalization of the fundamental theorem of calculus, called the (generalized) Stokes' theorem, which is a central result in the theory of integration on manifolds.