- is discontinuous at . This violates
assumptions in analytic methods which require be
approximated by a linear (trapezoidal), quadratic (Simpson) or
higher order polynomial.
- This assumption is violated by a function which is
discontinuous. Even if happens to be zero at , it would rarely have required zero derivatives (of
higher order for Gauss methods).
- On the other hand, Monte Carlo method only requires finite
standard deviation. If has NO requirement on continuity of
values; derivatives need not even exist.
- Thus, only Monte Carlo methods can use this ``bounding box'' approach to complicated integration domains. In practice, the latter are very common.

Geoffrey Fox, Northeast Parallel Architectures Center at Syracuse University, gcf@npac.syr.edu