  The Wodzicki residue and the cut-off integral extend to classical
symbol-valued forms. We show that they obey a Stokes' type property and that
the extended Wodzicki residue can be interpreted as a complex residue like the
ordinary one.
  In the case of cut-off integrals, Stokes' property (i.e. vanishing on exact
forms) only holds for non-integer order symbol-valued forms and leads to an
integration by parts formula and translation invariance for cut-off integrals
on non-integer order classical symbols.
  The extended Wodzicki residue yields an even residue cycle on classical
symbols and an odd cochain (the cosphere cochain) which measures an obstruction
to Stokes' property of the cut-off integral on integer order symbol-valued
forms.
