ABSTRACT
This chapter aims to develop tools to evaluate asymptotic integrals in terms of external numbers. It deals with integrals of internal functions over external intervals. These functions are supposed to be integrable in some classical sense, in particular Riemann-integrable or Lebesgue-integrable. The chapter considers integration for classes of flexible functions, which have internal integrable representatives, first over internal intervals, and then also over external intervals. Discontinuous flexible functions with jumps at external numbers cannot be inner-integrable, because they are not internally representable. The chapter shows that the integration of integrable functions reduces to the integration of an (internal) representative and the integration of a neutrix function, taking the sum of both. It also considers extensions of the Chasles Relation for dividing the interval of integration into two subintervals. Due to the existence of non-constant representative functions, the analogous formula on multiplication by an external number is less immediate.
