Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2014, 2(1), 1-5
DOI: 10.12691/tjant-2-1-1
Open AccessArticle

Application of Parseval’s Theorem on Evaluating Some Definite Integrals

Chii-Huei Yu1,

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

Pub. Date: January 16, 2014

Cite this paper:
Chii-Huei Yu. Application of Parseval’s Theorem on Evaluating Some Definite Integrals. Turkish Journal of Analysis and Number Theory. 2014; 2(1):1-5. doi: 10.12691/tjant-2-1-1

Abstract

This paper uses the mathematical software Maple for the auxiliary tool to study six types of definite integrals. We can determine the infinite series forms of these definite integrals by using Parseval’s theorem. On the other hand, we provide some definite integrals to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions using Maple.

Keywords:
definite integrals infinite series forms Parseval’s 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]  C. Oster, “Limit of a definite integral,” SIAM Review, vol. 33, no. 1, pp. 115-116, 1991.
 
[2]  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, pp. 253-260, Canada, 1999.
 
[3]  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.
 
[4]  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.
 
[5]  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.
 
[6]  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.
 
[7]  C. -H. Yu, “Evaluating some integrals with Maple,”International Journal of Computer Science and Mobile Computing, vol. 2, issue. 7, pp. 66-71, 2013.
 
[8]  C.-H. Yu, “Application of Maple on evaluation of definite integrals,”Applied Mechanics and Materials, vols. 479-480, pp. 823-827, 2013.
 
[9]  C. -H. Yu, “A study of some integral problems using Maple,” Mathematics and Statistics, vol. 2, no. 1, pp. 1-5, 2014.
 
[10]  C.-H. Yu, “Application of Maple on the integral problems,” Applied Mechanics and Materials, vols. 479-480, pp. 849-854, 2013.
 
[11]  C.-H. Yu,“Application of Maple on the integral problem of some type of rational functions, ”Proceedings of the Annual Meeting and Academic Conference for Association of IE, D357-D362, 2012.
 
[12]  C. -H. Yu, “Using Maple to study the integrals of trigonometric functions,”Proceedings of the 6th IEEE/International Conference on Advanced Infocomm Technology, no. 00294, 2013.
 
[13]  C.-H. Yu, “Application of Maple on some type of integral problem,”Proceedings of the Ubiquitous-Home Conference 2012, pp. 206-210, 2012.
 
[14]  C. -H. Yu,“A study of the integrals of trigonometric functions with Maple,”Proceedings of the Institute of Industrial Engineers Asian Conference 2013, Springer, vol. 1, pp. 603-610, 2013.
 
[15]  C.-H. Yu, “Application of Maple on some integral problems, ”Proceedings of the International Conference on Safety & Security Management and Engineering Technology 2012, pp. 290-294, 2012.
 
[16]  C.-H. Yu, “Application of Maple on evaluating the closed forms of two types of integrals,”Proceedings of the 17th Mobile Computing Workshop, ID16, 2012.
 
[17]  C.-H. Yu, “Application of Maple: taking two special integral problems as examples,”Proceedings of the 8th International Conference on Knowledge Community, pp. 803-811, 2012.
 
[18]  Hyperbolic functions, online available from http://en.wikipedia.org/wiki/Hyperbolic_function.
 
[19]  D. V. Widder, Advanced calculus, 2nd ed., Prentice-Hall, New Jersey, p 428, 1961.