<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we showed the linearity of the indefinite integral <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="forma.2006.14.issue-4_figure1.gif"></inline-graphic> the form of which was introduced in [11]. In addition, we proved some theorems about the integral calculus on the subinterval of [<italic>a,b</italic>]. As a result, we described the fundamental theorem of calculus, that we developed in [11], by a more general expression.</p></abstract>

In this paper, we showed the linearity of the indefinite integral  the form of which was introduced in [11]. In addition, we proved some theorems about the integral calculus on the subinterval of [a,b]. As a result, we described the fundamental theorem of calculus, that we developed in [11], by a more general expression.

Integrability and the Integral of Partial Functions from R into R<sup>1</sup>

Gifu National College of Technology, Gifu, Japan

Formalized Mathematics

Integrability and the Integral of Partial Functions from R into R

In this paper, we showed the linearity of the indefinite integral  the form of which was introduced in [11]. In addition, we proved some theorems about the...

Integrability and the Integral of Partial Functions from R into R¹

Published Online: Jun 13, 2008

Page range: 207 - 212

DOI: https://doi.org/10.2478/v10037-006-0023-y

This content is open access.

Integrability and the Integral of Partial Functions from R into R1

Published Online: Jun 13, 2008

Page range: 207 - 212

DOI: https://doi.org/10.2478/v10037-006-0023-y

This content is open access.

Integrability and the Integral of Partial Functions from R into R¹