Abstract
A Monte Carlo simulation program based on accompanying probability theory is developed and implemented to examine the trustworthiness of certain methods used in numerical integration. The power and reliability of an approximation process are defined. Using the simulation, estimated power and reliability values are obtained for the Trapezoidal rule, for Simpson’s rule, and for Romberg integration in conjunction with several frequently used stopping rules. The above-mentioned approximation processes are then analyzed and compared within the context of these two fundamental notions.
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