Abuse notation of improper integrals

Abstract

In the definition of , it was assumed that the interval [a, b] was finite. However, in many application in physics, engineering, economics, and probability we wish to allow a or b (or both) to be infinite or for the other case when f has an infinite discontinuity in [a, b]. In either case the integral is called improper integral. Definition of improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or ∞ or −∞ or, in some cases, as both endpoints approach limits. Many of the first-year students in ITERA learning about improper integrals make an abuse notation like written improper integral just like standard definite integral. Based on this situation, we tried to change the habits of the students in the writing of improper integrals by providing sufficient understanding and considerable exercises. It turns out this way gives good result, based on the percentage of the value of the midterms to the problem of improper integrals give a fairly good percentage value.