  We construct several sequences of asymptotically optimal definite quadrature
formulae of fourth order and evaluate their error constants. Besides the
asymptotical optimality, an advantage of our quadrature formulae is the
explicit form of their weights and nodes. For the remainders of our quadrature
formulae monotonicity properties are established when the integrand is a
4-convex function, and a-posteriori error estimates are proven.
