Henstock-Kurzweil Integral on [a,b]

Abstract

The theory of the Riemann integral was not fully satisfactory. Many important functions do not have a Riemann integral. So, Henstock and Kurzweil make the new theory of integral. From the background, the writer will be research about Henstock-Kurzweil integral and also theorems of Henstock- Kurzweil Integral. Henstock- Kurzweil Integral is generalized from Riemann integral. In this case the writer uses research methods literature or literature study carried out by way explore, observe, examine and identify the existing knowledge in the literature. In this thesis explain about partition which used in Henstock- Kurzweil Integral, definition and some property of Henstock- Kurzweil Integral. And some properties of Henstock- Kurzweil integral as follows: value of the Henstock- Kurzweil integral is unique, linearity of the Henstock-Kurzweil integral, Additivity of the Henstock-Kurzweil integral, Cauchy criteria, nonnegativity of Henstock-Kurzweil integral and primitive function.