This integral can not be solved analytically and therefore the solution is found using a numerical method" is something occasionally stumbled upon in the textbook of a first or second year calculus student. In this talk we will examine one of these numerical methods used to solve complex integration problems using a method known as "Monte Carlo Integration." This method is particularly useful for integration of higher dimensional functions but also computationally intensive making it very inefficient without the aid of the computer. Therefore, an implementation of this method in the R Programming Language will also be demonstrated.