Simpson's 3/8 Rule

$$\int_{x_1}^{x_4} f(x)\,dx = {\textstyle{3\over 8}} h (f_1+3f_2+3f_3+f_4) -{\textstyle{3\over 80}} h^5 f^{(4)}(\xi).$$

See also Bode's Rule, Newton-Cotes Formulas, Simpson's Rule

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 886, 1972.