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.
@article{bwmeta1.element.doi-10_2478_v10037-007-0007-6,
author = {Yasunari Shidama and Noboru Endou and Katsumi Wasaki},
title = {Riemann Indefinite Integral of Functions of Real Variable},
journal = {Formalized Mathematics},
volume = {15},
year = {2007},
pages = {59-63},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-007-0007-6}
}
Yasunari Shidama; Noboru Endou; Katsumi Wasaki. Riemann Indefinite Integral of Functions of Real Variable. Formalized Mathematics, Tome 15 (2007) pp. 59-63. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-007-0007-6/
[7] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
[8] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
[9] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
[10] Czesław Byliński and Piotr Rudnicki. Bounding boxes for compact sets in ε2. Formalized Mathematics, 6(3):427-440, 1997.
[11] Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93-102, 1999.
[12] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions. Formalized Mathematics, 9(2):281-284, 2001.
[13] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
[14] Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Formalized Mathematics, 1(3):477-481, 1990.
[15] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.
[16] Jarosław Kotowicz. Partial functions from a domain to the set of real numbers. Formalized Mathematics, 1(4):703-709, 1990.
[17] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
[18] Beata Perkowska. Functional sequence from a domain to a domain. Formalized Mathematics, 3(1):17-21, 1992.
[19] Konrad Raczkowski and Paweł Sadowski. Real function continuity. Formalized Mathematics, 1(4):787-791, 1990.
[20] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.
[21] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
[22] Yasunari Shidama. The Taylor expansions. Formalized Mathematics, 12(2):195-200, 2004.
[23] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
[24] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
[25] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
[26] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
[27] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998.
[1] Tom M. Apostol. Mathematical Analysis. Addison-Wesley, 1969.
[2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. | Zbl 06213858
[3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
[4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
[5] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
[6] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.