For example, consider black curve on the interval , so that , , and. Then Simpson's rule which corresponds to the area under the blue curve obtained from the third-order interpolating polynomial gives. An extended version of the rule can be written for tabulated at , , Abramowitz, M. New York: Dover, p. Horwitz, A. Jeffreys, H. Methods of Mathematical Physics, 3rd ed.
Cambridge, England: Cambridge University Press, p. Trott, M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, p. Whittaker, E. New York: Dover, pp.
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