Based on the dominated convergence theorem and parametric differentiation, two different evaluations of the Laplace integral are displayed. This article presents two different proofs of (1) which may be of interest since they are based on principles within the realm of real analysis. The first method applies the dominated convergence theorem to an integral sequence. The second method uses an ordinary differential equation based on parametric differentiation. It is interesting to see how wide a range of analysis topics are exploited. These evaluations provide a nice application of the dominated convergence theorem and parametric differentiation.