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

Abstract

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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.

How to cite

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Yasunari 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

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  1. [7] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  2. [8] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  3. [9] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990. 
  4. [10] Czesław Byliński and Piotr Rudnicki. Bounding boxes for compact sets in ε2. Formalized Mathematics, 6(3):427-440, 1997. 
  5. [11] Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93-102, 1999. 
  6. [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. 
  7. [13] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990. 
  8. [14] Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Formalized Mathematics, 1(3):477-481, 1990. 
  9. [15] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990. 
  10. [16] Jarosław Kotowicz. Partial functions from a domain to the set of real numbers. Formalized Mathematics, 1(4):703-709, 1990. 
  11. [17] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990. 
  12. [18] Beata Perkowska. Functional sequence from a domain to a domain. Formalized Mathematics, 3(1):17-21, 1992. 
  13. [19] Konrad Raczkowski and Paweł Sadowski. Real function continuity. Formalized Mathematics, 1(4):787-791, 1990. 
  14. [20] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990. 
  15. [21] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990. 
  16. [22] Yasunari Shidama. The Taylor expansions. Formalized Mathematics, 12(2):195-200, 2004. 
  17. [23] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics. 
  18. [24] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990. 
  19. [25] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  20. [26] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 
  21. [27] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998. 
  22. [1] Tom M. Apostol. Mathematical Analysis. Addison-Wesley, 1969. 
  23. [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
  24. [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  25. [4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  26. [5] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990. 
  27. [6] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990. 

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