  In this paper we consider the problem of the calculus of variations for a
functional which is the composition of a certain scalar function $H$ with the
delta integral of a vector valued field $f$, i.e., of the form
$H(\int_{a}^{b}f(t,x^{\sigma}(t),x^{\Delta}(t))\Delta t)$. Euler-Lagrange
equations, natural boundary conditions for such problems as well as a necessary
optimality condition for isoperimetric problems, on a general time scale, are
given. A number of corollaries are obtained, and several examples illustrating
the new results are discussed in detail.
