If M is an -dimensional manifold in Rn, with the usual orientation, show that dV = dx1^

Question:

If M is an -dimensional manifold in Rn, with the usual orientation, show that dV = dx1^ . . . ^ dxn, so that the volume of M, as defined in this section, is the volume as defined in Chapter 3. (Note that this depends on the numerical factor in the definition of w ^ n.)