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 / i

Use Simpson's rule: the cubic exactness of Simpson's rule includes every quadratic integrand, so three function evaluations already give the exact answer. Thus the error is zero. For a general smooth integrand the corresponding composite Simpson's rule has error $O(N^{-4})$ in big O notation, but that bound is unnecessarily weak here.