Abstract
A generalization of the modified Simpson's rule is derived. Various error bounds for this generalization are established. An application to Dawson integral is given. References G. A. Anastassiou, Ostrowski type inequalities, Proc. Amer. Math. Soc., Vol. 123(12), (1995), 3775--3781. P. Cerone and S. S. Dragomir, Midpoint-type rules from an inequalities point of view, handbook of analytic-computational methods in applied mathematics, Editor: G. Anastassiou, CRC Press, New York, (2000), 135--200. P. Cerone and S. S. Dragomir, Trapezoidal-type rules from an inequalities point of view, handbook of analytic-computational methods in applied mathematics, Editor: G. Anastassiou, CRC Press, New York, (2000), 65--134. Lj. Dedic, M. Matic and J. Pecaric, On Euler trapezoid formulae, Appl. Math. Comput., 123 (2001), 37--62. http://dx.doi.org/10.1016/S0096-3003(00)00054-0 C. E. M. Pearce, J. Pecaric, N. Ujevic and S. Varosanec, Generalizations of some inequalities of Ostrowski--Gruss type, Math. Inequal. Appl., 3(1), (2000), 25--34. http://www.mia-journal.com/files/3-1/full/03-03.PDF N. Ujevic and A. J. Roberts, A corrected quadrature formula and applications, ANZIAM J., 45(E), (2004), E41--E56. http://anziamj.austms.org.au/V45/E051
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