= Solution
\b[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.
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