  In this work we establish a Stokes-type integral equality for scalarly
essentially integrable forms on an orientable smooth manifold with values in
the locally convex linear space $\langle B(G),\sigma(B(G),\mathcal{N})\rangle$,
where $G$ is a complex Banach space and $\mathcal{N}$ is a suitable linear
subspace of the norm dual of $B(G)$. This result widely extends the
Newton-Leibnitz-type equality stated in one of our previous articles. To obtain
our equality we generalize the main result of that article, and employ the
Stokes theorem for smooth locally convex vector valued forms established in a
prodromic paper. Two facts are remarkable. Firstly the forms integrated
involved in the equality are functions of a possibly unbounded scalar type
spectral operator in $G$. Secondly these forms need not be smooth nor even
continuously differentiable.
