American Journal of Systems and Software
ISSN (Print): 2372-708X ISSN (Online): 2372-7071 Website: http://www.sciepub.com/journal/ajss Editor-in-chief: Josué-Antonio Nescolarde-Selva
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American Journal of Systems and Software. 2014, 2(4), 85-88
DOI: 10.12691/ajss-2-4-1
Open AccessArticle

Evaluation of Triple Integrals

Chii-Huei Yu1, and Shinn-Der Sheu2

1Department of Management and Information, Nan Jeon University of Science and Technology, Tainan City, Taiwan

2Department of Information Technology, Nan Jeon University of Science and Technology, Tainan City, Taiwan

Pub. Date: July 04, 2014

Cite this paper:
Chii-Huei Yu and Shinn-Der Sheu. Evaluation of Triple Integrals. American Journal of Systems and Software. 2014; 2(4):85-88. doi: 10.12691/ajss-2-4-1

Abstract

This article considers two types of triple integrals and uses Maple for verification. The infinite series forms of the two types of triple integrals can be obtained using binomial series and integration term by term theorem. In addition, some examples are used to demonstrate the calculations.

Keywords:
triple integrals infinite series forms binomial series integration term by term theorem Maple

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  A. A. Adams, H. Gottliebsen, S. A. Linton, and U. Martin, “Automated theorem proving in support of computer algebra: symbolic definite integration as a case study,” Proceedings of the 1999 International Symposium on Symbolic and Algebraic Computation, Canada, pp. 253-260, 1999.
 
[2]  M. A. Nyblom, “On the evaluation of a definite integral involving nested square root functions,” Rocky Mountain Journal of Mathematics, Vol. 37, No. 4, pp. 1301-1304, 2007.
 
[3]  C. Oster, “Limit of a definite integral,” SIAM Review, Vol. 33, No. 1, pp. 115-116, 1991.
 
[4]  C. -H. Yu, “A study of two types of definite integrals with Maple,” Jökull Journal, Vol. 64, No. 2, pp. 543-550, 2014.
 
[5]  C. -H. Yu, “Evaluating two types of definite integrals using Parseval’s theorem,” Wulfenia Journal, Vol. 21, No. 2, pp. 24-32, 2014.
 
[6]  C. -H. Yu, “Solving some definite integrals using Parseval’s theorem,” American Journal of Numerical Analysis, Vol. 2, No. 2, pp. 60-64, 2014.
 
[7]  C. -H. Yu, “Some types of integral problems,” American Journal of Systems and Software, Vol. 2, No. 1, pp. 22-26, 2014.
 
[8]  C. -H. Yu, “Using Maple to study the double integral problems,” Applied and Computational Mathematics, Vol. 2, No. 2, pp. 28-31, 2013.
 
[9]  C. -H. Yu, “A study on double Integrals,” International Journal of Research in Information Technology, Vol. 1, Issue. 8, pp. 24-31, 2013.
 
[10]  C. -H. Yu, “Application of Parseval’s theorem on evaluating some definite integrals,” Turkish Journal of Analysis and Number Theory, Vol. 2, No. 1, pp. 1-5, 2014.
 
[11]  C. -H. Yu, “Evaluation of two types of integrals using Maple, ”Universal Journal of Applied Science, Vol. 2, No. 2, pp. 39-46, 2014.
 
[12]  C. -H. Yu, “Studying three types of integrals with Maple, ”American Journal of Computing Research Repository, Vol. 2, No. 1, pp. 19-21, 2014.
 
[13]  C. -H. Yu, “The application of Parseval’s theorem to integral problems,” Applied Mathematics and Physics, Vol. 2, No. 1, pp. 4-9, 2014.
 
[14]  C. -H. Yu, “A study of some integral problems using Maple,” Mathematics and Statistics, Vol. 2, No. 1, pp. 1-5, 2014.
 
[15]  C. -H. Yu, “Solving some definite integrals by using Maple, ”World Journal of Computer Application and Technology, Vol. 2, No. 3, pp. 61-65, 2014.
 
[16]  C. -H. Yu, “Using Maple to study two types of integrals,” International Journal of Research in Computer Applications and Robotics, Vol. 1, Issue. 4, pp. 14-22, 2013.
 
[17]  C. -H. Yu, “Solving some integrals with Maple,” International Journal of Research in Aeronautical and Mechanical Engineering, Vol. 1, Issue. 3, pp. 29-35, 2013.
 
[18]  C. -H. Yu, “A study on integral problems by using Maple, ”International Journal of Advanced Research in Computer Science and Software Engineering, Vol. 3, Issue. 7, pp. 41-46, 2013.
 
[19]  C. -H. Yu, “Evaluating some integrals with Maple,” International Journal of Computer Science and Mobile Computing, Vol. 2, Issue. 7, pp. 66-71, 2013.
 
[20]  C. -H. Yu, “Application of Maple on evaluation of definite integrals,” Applied Mechanics and Materials, Vols. 479-480 (2014), pp. 823-827, 2013.
 
[21]  C. -H. Yu, “Application of Maple on the integral problems,” Applied Mechanics and Materials, Vols. 479-480 (2014), pp. 849-854, 2013.
 
[22]  C. -H. Yu, “Using Maple to study the integrals of trigonometric functions,” Proceedings of the 6th IEEE/International Conference on Advanced Infocomm Technology, Taiwan, No. 00294, 2013.
 
[23]  C. -H. Yu, “A study of the integrals of trigonometric functions with Maple,” Proceedings of the Institute of Industrial Engineers Asian Conference 2013, Taiwan, Springer, Vol. 1, pp. 603-610, 2013.
 
[24]  C. -H. Yu, “Application of Maple on the integral problem of some type of rational functions,” (in Chinese) Proceedings of the Annual Meeting and Academic Conference for Association of IE, Taiwan, D357-D362, 2012.
 
[25]  C. -H. Yu, “Application of Maple on some integral problems, ”(in Chinese) Proceedings of the International Conference on Safety & Security Management and Engineering Technology 2012, Taiwan, pp. 290-294, 2012.
 
[26]  C. -H. Yu, “Application of Maple on some type of integral problem,” (in Chinese) Proceedings of the Ubiquitous-Home Conference 2012, Taiwan, pp. 206-210, 2012.
 
[27]  C. -H. Yu, “Application of Maple on evaluating the closed forms of two types of integrals,” (in Chinese) Proceedings of the 17th Mobile Computing Workshop, Taiwan, ID16, 2012.
 
[28]  C. -H. Yu, “Application of Maple: taking two special integral problems as examples,” (in Chinese) Proceedings of the 8th International Conference on Knowledge Community, Taiwan, pp. 803-811, 2012.
 
[29]  C. -H. Yu, “Evaluating some types of definite integrals,” American Journal of Software Engineering, Vol. 2, Issue. 1, pp. 13-15, 2014.
 
[30]  C. -H. Yu and B. -H. Chen, “Solving some types of integrals using Maple,” Universal Journal of Computational Mathematics, Vol. 2, No. 3, pp. 39-47, 2014.
 
[31]  C. -H. Yu and S. -D. Sheu “Infinite series forms of double integrals,” International Journal of Data Envelopment Analysis and *Operations Research*, Vol. 1, No. 2, pp. 16-20, 2014.
 
[32]  C. -H. Yu and S. -D. Sheu “Using area mean value theorem to solve some double integrals,” Turkish Journal of Analysis and Number Theory, Vol. 2, No. 3, pp. 75-79, 2014.
 
[33]  T. -J. Chen and C. -H. Yu, “A study on the integral problems of trigonometric functions using two methods,” Wulfenia Journal, Vol. 21, No. 4, pp. 76-86, 2014.
 
[34]  T. -J. Chen and C. -H. Yu, “Fourier series expansions of some definite integrals,” Sylwan Journal, Vol. 158, Issue. 5, pp. 124-131, 2014.
 
[35]  T. -J. Chen and C. -H. Yu, “Evaluating some definite integrals using generalized Cauchy integral formula,” Mitteilungen Klosterneuburg, Vol. 64, Issue. 5, pp. 52-63, 2014.
 
[36]  T. M. Apostol, Mathematical analysis (2nd ed.), Addison-Wesley, Massachusetts, 1975.