Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Discrete mathematics, continuous mathematics, and probability / Continuous mathematics / 5 / a / ii / Solution

Use composite Simpson's rule on this smooth, bounded one-dimensional interval. Its fourth derivative is bounded on the interval, so the error bound for composite Simpson's rule gives $O(N^{-4})$ in big O notation as the number of function evaluations increases.