Allowable Changes of Variable for Recently Developed Improper Integral Definitions

Sufficient conditions for performing changes of the variable of integration when using the new definitions of improper integrals given in in “An Alternative Definition for Improper Integral with Infinite Limit” (arXiv:0805.3559v1) and “An Alternative Definition for Improper Integral with Finite Limits” (arXiv:0810.4654v1) are presented. These changes of variable are valid when both the initial and final integrals exist. In general, the existence of one of the integrals does not guarantee the existence of the other. In a restricted set of changes of variable, the existence of either integral guarantees existence of the other.