In this work, geometric algebra is applied to obtain the volume-element of integration for the 3 Cartesian coordinates of the center-of-mass, 3 Euler angles, and 3N-6 shape coordinates needed to describe the position, orientation, and shape of an N-atomic molecule. The volume-element is obtained as a product of N volume-elements, each associated with a set of three coordinates. The method presented has several advantages. For example, one does not need to expand any determinants, and all calculations are performed in the three-dimensional physical space (not in some 3N-dimensional abstract configuration space). Several examples and applications are given.