Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Discrete mathematics, continuous mathematics, and probability / 4 / e / Solution

No: Monte Carlo integration is poorly suited to this smooth one-dimensional problem at such a tight tolerance. A sample-average Monte Carlo estimator has a standard error proportional to $N^{-1/2}$, whereas the deterministic composite Simpson's rule bound decreases as $n^{-4}$ here and already certifies the target with tens of strips. Random sampling would require vastly more function evaluations and supplies a probabilistic error statement rather than the displayed deterministic guarantee.