  We provide sufficient conditions for the existence of a strong derivable map
and calculate its derivative by employing a result in our previous work on
strong derivability of maps arising by functional calculus of an unbounded
scalar type spectral operator $R$ in a Banach space and the generalization to
complete locally convex spaces of a classical result valid in the Banach space
context. We apply this result to obtain a sequence of integrals converging to
an integral of a complete locally convex space extension of a map arising by
functional calculus of $R$.
