A novel approach to evaluating improper integrals

Abstract

Abstract. We explain and apply a recently developed method for evaluating improper integrals of the form \( \int_{0}^{\infty} f(t) \, dt \) using Laplace transforms. A number of examples are provided to illustrate the method, along with some results that streamline the computations. We show how the method can be used to readily determine values for entire classes of certain integrals which, using other more familiar methods, are difficult to find. We also indicate how the method can determine the values of integrals for which other methods fail.