Improper Integrals of Real Functions : Print this page First   |   Last   |   Prev   |   Next Note: It is important to note the following: If the improper integral converges, then the Cauchy principal value exists. Further, . When the Cauchy principal value exists, it is not always true that converges. For example, exists, but fails to exist. If is an even function on (That is, for all ) and if the Cauchy principal value exists, then the improper integral exists and equal to . Note: If is not an even function, then it is always a good practice to write explicitly before the integral symbol to denote the Cauchy principal value of the improper integral. First   |   Last   |   Prev   |   Next