Integral mean value theorem for discontinuous function

Abstract

This study examines the modification of the integral mean value theorem for discontinuous functions. Modification is studied by proving that a function that is not continuous at a certain and bounded interval can be integrated (finite integral) both in Rieman’s integral and Newton’s integral (integral as antiderivative). The discontinuity of the intended function, namely; f is defined on [a,b] but the value of a function and its limit are not equal at some points or infinite points and countable on (a,b), f is undefined on [a,b] at some points or infinite points and countable on (a,b) but its limit exists there. The results of this study provide a modification of the integral mean value theorem by replacing the value of f in the implication of the theorem with its limit value so that the integral mean value theorem is obtained for the non-continuous function.