It is also possible to integrate forms of other degrees along the fibers of a submersion. Assume the same hypotheses as before, and let be a compactly supported -form on . Then there is a -form on which is the result of integrating along the fibers of . The form is defined by specifying, at each , how pairs against each -vector at , and the value of that pairing is an integral over that depends only on , , and the orientations of and . More precisely, at each , there is an isomorphism