Riemann Indefinite Integral of Functions of Real Variable

Yasunari Shidama; Noboru Endou; Katsumi Wasaki

doi:10.2478/v10037-007-0007-6

.blurhash-client-img { display: none !important; }

Riemann Indefinite Integral of Functions of Real Variable

Formalized Mathematics

Volume 15 (2007): Issue 2 (June 2007)

By: Yasunari Shidama, Noboru Endou and Katsumi Wasaki

Open Access

|Jun 2008

Abstract

In this article we define the Riemann indefinite integral of functions of real variable and prove the linearity of that [1]. And we give some examples of the indefinite integral of some elementary functions. Furthermore, also the theorem about integral operation and uniform convergent sequence of functions is proved.

References

[7] Czesław Byliński. Functions from a set to a set., 1(1):153-164, 1990.
Search in Google Scholar
[8] Czesław Byliński. Partial functions., 1(2):357-367, 1990.
Search in Google Scholar
[9] Czesław Byliński. The sum and product of finite sequences of real numbers., 1(4):661-668, 1990.
Search in Google Scholar
[10] Czesław Byliński and Piotr Rudnicki. Bounding boxes for compact sets in ε., 6(3):427-440, 1997.
Search in Google Scholar
[11] Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas., 8(1):93-102, 1999.
Search in Google Scholar
[12] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions., 9(2):281-284, 2001.
Search in Google Scholar
[13] Krzysztof Hryniewiecki. Basic properties of real numbers., 1(1):35-40, 1990.
Search in Google Scholar
[14] Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers., 1(3):477-481, 1990.
Search in Google Scholar
[15] Jarosław Kotowicz. Convergent sequences and the limit of sequences., 1(2):273-275, 1990.
Search in Google Scholar
[16] Jarosław Kotowicz. Partial functions from a domain to the set of real numbers., 1(4):703-709, 1990.
Search in Google Scholar
[17] Jarosław Kotowicz. Real sequences and basic operations on them., 1(2):269-272, 1990.
Search in Google Scholar
[18] Beata Perkowska. Functional sequence from a domain to a domain., 3(1):17-21, 1992.
Search in Google Scholar
[19] Konrad Raczkowski and Paweł Sadowski. Real function continuity., 1(4):787-791, 1990.
Search in Google Scholar
[20] Konrad Raczkowski and Paweł Sadowski. Real function differentiability., 1(4):797-801, 1990.
Search in Google Scholar
[21] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers., 1(4):777-780, 1990.
Search in Google Scholar
[22] Yasunari Shidama. The Taylor expansions., 12(2):195-200, 2004.
Search in Google Scholar
[23] Andrzej Trybulec. Subsets of complex numbers.
Search in Google Scholar
[24] Andrzej Trybulec. Tarski Grothendieck set theory., 1(1):9-11, 1990.
Search in Google Scholar
[25] Zinaida Trybulec. Properties of subsets., 1(1):67-71, 1990.
Search in Google Scholar
[26] Edmund Woronowicz. Relations defined on sets., 1(1):181-186, 1990.
Search in Google Scholar
[27] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio., 7(2):255-263, 1998.
Search in Google Scholar
[1] Tom M. Apostol.Addison-Wesley, 1969.
Search in Google Scholar
[2] Grzegorz Bancerek. The fundamental properties of natural numbers., 1(1):41-46, 1990.
Search in Google Scholar
[3] Grzegorz Bancerek. The ordinal numbers., 1(1):91-96, 1990.
Search in Google Scholar
[4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences., 1(1):107-114, 1990.
Search in Google Scholar
[5] Czesław Byliński. The complex numbers., 1(3):507-513, 1990.
Search in Google Scholar
[6] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets., 1(3):529-536, 1990.
Search in Google Scholar