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We construct several sequences of asymptotically optimal definite quadratureformulae of fourth order and evaluate their error constants. Besides theasymptotical optimality, an advantage of our quadrature formulae is theexplicit form of their weights and nodes. For the remainders of our quadratureformulae monotonicity properties are established when the integrand is a4-convex function, and a-posteriori error estimates are proven.

Asymptotically optimal definite quadrature formulae of $4$-th order