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We develop the calculus of variations on time scales for a functional that isthe composition of a certain scalar function with the delta and nabla integralsof a vector valued field. Euler-Lagrange equations, transversality conditions,and necessary optimality conditions for isoperimetric problems, on an arbitrarytime scale, are proved. Interesting corollaries and examples are presented.

The Delta-nabla Calculus of Variations for Composition Functionals on Time Scales