Riemann Indefinite Integral of Functions of Real Variable
Yasunari Shidama; Noboru Endou; Katsumi Wasaki
Formalized Mathematics (2007)
- Volume: 15, Issue: 2, page 59-63
- ISSN: 1426-2630
Access Full Article
topAbstract
topHow to cite
topYasunari Shidama, Noboru Endou, and Katsumi Wasaki. "Riemann Indefinite Integral of Functions of Real Variable." Formalized Mathematics 15.2 (2007): 59-63. <http://eudml.org/doc/267359>.
@article{YasunariShidama2007,
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.},
author = {Yasunari Shidama, Noboru Endou, Katsumi Wasaki},
journal = {Formalized Mathematics},
language = {eng},
number = {2},
pages = {59-63},
title = {Riemann Indefinite Integral of Functions of Real Variable},
url = {http://eudml.org/doc/267359},
volume = {15},
year = {2007},
}
TY - JOUR
AU - Yasunari Shidama
AU - Noboru Endou
AU - Katsumi Wasaki
TI - Riemann Indefinite Integral of Functions of Real Variable
JO - Formalized Mathematics
PY - 2007
VL - 15
IS - 2
SP - 59
EP - 63
AB - 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.
LA - eng
UR - http://eudml.org/doc/267359
ER -
References
top- [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. Zbl06213858
- [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.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.