Open AccessIntegral mean value theorem for discontinuous function
Author(s) -
Ovan,
Andika Saputra,
N Tasni
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1918/4/042033
Subject(s) - mathematics , mean value theorem (divided differences) , daniell integral , riemann integral , improper integral , countable set , green's theorem , limit (mathematics) , bounded function , mathematical analysis , fundamental theorem of calculus , discontinuity (linguistics) , line integral , continuous function (set theory) , multiple integral , kelvin–stokes theorem , function (biology) , integral equation , pure mathematics , picard–lindelöf theorem , fixed point theorem , danskin's theorem , fourier integral operator , evolutionary biology , biology
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.