A Study of Definite Integrals Using Parseval's Identity

Authors

  • Chii-Huei Yu  Department of Information Technology, Nan Jeon University of Science and Technology, Taiwan

Keywords:

Definite Integrals, Parsevals Identity, Infinite Series Expressions, Maple.

Abstract

This paper studies two types of definite integrals. Using Parseval's identity, we can determine the infinite series expressions of the two types of definite integrals. Moreover, we propose two examples to do calculation practically. The research method adopted in this study is to find solutions through manual calculations and verify these solutions using Maple. This research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking. For this reason, Maple provides insights and guidance regarding problem-solving methods.

References

  1. 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. 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. Oster, “Limit of a definite integral,”SIAM Review, Vol. 33, No. 1, pp. 115-116, 1991.
  4. -H. Yu,“Solving some definite integrals using Parseval’s theorem,”American Journal of Numerical Analysis, Vol. 2, No. 2, pp. 60-64, 2014.
  5. -H. Yu,“Some types of integral problems,”American Journal of Systems and Software, Vol. 2, No. 1, pp. 22-26, 2014.
  6. -H. Yu,“Using Maple to study the double integral problems,” Applied and Computational Mathematics, Vol. 2, No. 2, pp. 28-31, 2013.
  7. -H. Yu, “ A study on double Integrals, ” International Journal of Research in Information Technology, Vol. 1, Issue. 8, pp. 24-31, 2013.
  8. -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.
  9. -H. Yu, “Evaluation of two types of integrals using Maple, ”Universal Journal of Applied Science, Vol. 2, No. 2, pp. 39-46, 2014.
  10. -H. Yu, “Studying three types of integrals with Maple, ”American Journal of Computing Research Repository, Vol. 2, No. 1, pp. 19-21, 2014.
  11. -H. Yu, “The application of Parseval’s theorem to integral problems,”Applied Mathematics and Physics, Vol. 2, No. 1, pp. 4-9, 2014.
  12. -H. Yu, “A study of some integral problems using Maple, ”Mathematics and Statistics, Vol. 2, No. 1, pp. 1-5, 2014.
  13. -H. Yu, “Solving some definite integrals by using Maple,”World Journal of Computer Application and Technology, Vol. 2, No. 3, pp. 61-65, 2014.
  14. -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.
  15. -H. Yu, “Solving some integrals with Maple,”International Journal of Research in Aeronautical and Mechanical Engineering, Vol. 1, Issue. 3, pp. 29-35, 2013.
  16. -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.
  17. -H. Yu,“Evaluating some integrals with Maple,” International Journal of Computer Science and Mobile Computing, Vol. 2, Issue. 7, pp. 66-71, 2013.
  18. -H. Yu, “Application of Maple on evaluation of definite integrals,”Applied Mechanics and Materials, Vols. 479-480 (2014), pp. 823-827, 2013.
  19. -H. Yu, “Application of Maple on the integral problems, ”Applied Mechanics and Materials, Vols. 479-480 (2014), pp. 849-854, 2013.
  20. -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.
  21. -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.
  22. -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.
  23. -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.
  24. -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.
  25. -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.
  26. -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.
  27. -H. Yu, “Evaluating some types of definite integrals, ”American Journal of Software Engineering, Vol. 2, Issue. 1, pp. 13-15, 2014.
  28. -H. Yu, “Calculating Some Integrals of Trigonometric Functions,” International Journal of Research, Vol. 3, Issue. 8, pp. 57-63, 2016.
  29. -H. Yu, “Application of a Complex Integral Formula,” International Journal of Information Technology, Vol. 11, No. 1, pp. 288-293, 2016.
  30. -H. Yu, “The Solutions of Some Real Definite Integrals,” International Journal of Information Technology, Vol. 11, No. 1, pp. 209-214, 2016.
  31. -H. Yu, “A Study of an Integral Related to the Logarithmic Function with Maple,” International Journal of Research, Vol. 3, Issue. 1, pp. 1049-1054, 2016.
  32. -H. Yu, “Solving Real Integrals Using Complex Integrals,” International Journal of Research, Vol. 3, Issue. 4, pp. 95-100, 2016.
  33. -H. Yu, “Integral Problems of Trigonometric Functions,” International Journal of Scientific Research in Science and Technology, Vol. 2, Issue. 1, pp. 63-67, 2016.
  34. -H. Yu, “Application of Complex Analysis on Solving Some Definite Integrals,” International Journal of Mathematical Engineering and Science, Vol. 3, Issue. 3, pp. 11-20, 2014.
  35. -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.
  36. -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.
  37. -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.
  38. -H. Yu and S. -D. Sheu, “Evaluation of triple integrals,” American Journal of Systems and Software, Vol. 2, No. 4, pp. 85-88, 2014.

Downloads

Published

2016-10-30

Issue

Section

Research Articles

How to Cite

[1]
Chii-Huei Yu, " A Study of Definite Integrals Using Parseval's Identity, IInternational Journal of Scientific Research in Computer Science, Engineering and Information Technology(IJSRCSEIT), ISSN : 2456-3307, Volume 1, Issue 2, pp.28-32, September-October-2016.