As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of mathematics. The choice of the probability density function determines the form of the integral giving the expectation and thus the time the basic program runs and its accuracy. This is a nice incentive for students. The more they know about probability, the better that they are at numerical analysis.