Introduction
In this insight article, we will build all the machinery necessary to evaluate unit hypercube integrals by a novel technique. We will first state a theorem on Dirichlet integrals, second develop a sequence of nested sets that point-wise converges to a unit hypercube, and thirdly make these two pieces compatible by means of a Dominated Convergence Theorem, and lastly demonstrate the technique of integration. Note: The same technique is outlined (in the same way) in the expanded insight article entitled A Path to Fractional Integral Representations of Some Special Functions.
The Integrals of Dirichlet
Dirichlet integrals as I learned them from an Advanced Calculus book are just that formula evaluating the integral to Gamma functions, they are not a type of integral like Riemann integral, more just a formula that would go on a table of...