Integral Problems of Trigonometric Functions

Authors

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

Keywords:

Integrals, Trigonometric Functions, Infinite Series Expressions, Taylor Series Expansions, Integration Term by Term Theorem, Maple

Abstract

The article considers six types of integrals related with the powers of trigonometric functions. We can obtain the infinite series expressions of these integrals by using Taylor series expansions and integration term by term theorem. Moreover, we propose some integrals to do calculation and evaluate some definite integrals practically. On the other hand, Maple is used to calculate the approximations of these definite integrals and their infinite series expressions for verifying our answers.

References

  1. Adams, A. A., Gottliebsen, H., Linton, S. A., and Martin, U., 1999. 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, 253-260.
  2. Nyblom, M. A., 2007. On the evaluation of a definite integral involving nested square root functions, Rocky Mountain Journal of Mathematics, 37(4), 1301-1304.
  3. Oster, C., 1991. Limit of a definite integral, SIAM Review, 33(1), 115-116.
  4. Yu, C. -H., 2014. Solving some definite integrals using Parseval’s theorem, American Journal of Numerical Analysis, 2(2), 60-64.
  5. Yu, C. -H., 2014. Some types of integral problems, American Journal of Systems and Software, 2(1), 22-26.
  6. Yu, C. -H., 2014. Application of Parseval’s theorem on evaluating some definite integrals, Turkish Journal of Analysis and Number Theory, 2(1), 1-5.
  7. Yu, C. -H., 2014. Evaluation of two types of integrals using Maple, Universal Journal of Applied Science, 2(2), 39-46.
  8. Yu, C. -H., 2014. Studying three types of integrals with Maple, American Journal of Computing Research Repository, 2(1), 19-21.
  9. Yu, C. -H., 2014. The application of Parseval’s theorem to integral problems, Applied Mathematics and Physics, 2(1), 4-9.
  10. Yu, C. -H., 2014. A study of some integral problems using Maple, Mathematics and Statistics, 2(1), 1-5.
  11. Yu, C. -H., 2014. Solving some definite integrals by using Maple, World Journal of Computer Application and Technology, 2(3), 61-65.
  12. Yu, C. -H., 2014. Evaluating some types of definite integrals, American Journal of Software Engineering, 2(1), 13-15.
  13. Yu, C. -H., 2013. Using Maple to study two types of integrals, International Journal of Research in Computer Applications and Robotics, 1(4), 14-22.
  14. Yu, C. -H., 2013. Solving some integrals with Maple, International Journal of Research in Aeronautical and Mechanical Engineering, Vol. 1(3), pp. 29-35.
  15. Yu, C. -H., 2013. A study on integral problems by using Maple, International Journal of Advanced Research in Computer Science and Software Engineering, 3(7), 41-46.
  16. Yu, C. -H., 2013. Evaluating some integrals with Maple, International Journal of Computer Science and Mobile Computing, 2(7), 66-71.
  17. Yu, C. -H., 2013. Application of Maple on evaluation of definite integrals, Applied Mechanics and Materials, 479-480, 823-827.
  18. Yu, C. -H., 2013. Application of Maple on the integral problems, Applied Mechanics and Materials, 479-480, 849-854.
  19. Yu, C. -H., 2013. Using Maple to study multiple improper integrals, International Journal of Research in Information Technology, 1(8), 10-14.
  20. Yu, C. -H., 2013. A study on the multiple improper integral problems, (in Chinese) Journal of Hsin Sheng, 12, 175-194.
  21. Yu, C. -H., 2013. Application of Maple: the evaluation of double integral as an example, (in Chinese) Proceedings of 2013 International Symposium on Intercultural Communication, Taiwan, 294-302.
  22. Yu, C. -H., 2013. Using Maple to study the double integral problems, Applied and Computational Mathematics, 2(2), 28-31.
  23. Yu, C. -H., 2013. A study on double integrals, International Journal of Research in Information Technology, 1(8), 24-31.
  24. Yu, C. -H., 2013. Using Maple to study the integrals of trigonometric functions, Proceedings of the 6th IEEE/International Conference on Advanced Infocomm Technology, Taiwan, No. 00294.
  25. Yu, C. -H., 2013. A study of the integrals of trigonometric functions with Maple, Proceedings of the Institute of Industrial Engineers Asian Conference 2013, Taiwan, Springer,  1, 603-610.
  26. Yu, C. -H., 2013. Application of Maple on evaluating the double improper integrals, (in Chinese) Proceedings of the Innovative Education and Learning Technology, Taiwan, 75-84.
  27. Yu, C. -H., 2012. 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.
  28. Yu, C. -H., 2012. Application of Maple on some integral problems, (in Chinese) Proceedings of the International Conference on Safety & Security Management and Engineering Technology 2012, Taiwan, 290-294.
  29. Yu, C. -H., 2012. Application of Maple on some type of integral problem, (in Chinese) Proceedings of the Ubiquitous-Home Conference 2012, Taiwan, 206-210.
  30. Yu, C. -H., 2012. Application of Maple on evaluating the closed forms of two types of integrals, (in Chinese) Proceedings of the 17th Mobile Computing Workshop, Taiwan, ID16.
  31. Yu, C. -H., 2012. Application of Maple: taking two special integral problems as examples, (in Chinese) Proceedings of the 8th International Conference on Knowledge Community, Taiwan, 803-811.
  32. Yu, C. -H. and Chen, B. -H., 2014. Solving some types of integrals using Maple, Universal Journal of Computational Mathematics, 2(3), 39-47.
  33. Yu, C. -H. and Sheu, S. -D, 2014. Using area mean value theorem to solve some double integrals, Turkish Journal of Analysis and Number Theory, 2(3), 75-79.
  34. Yu, C. -H. and Sheu, S. -D, 2014. Infinite series forms of double integrals, International Journal of Data Envelopment Analysis and *Operations Research*, 1(2), 16-20.
  35. Yu, C. -H. and Sheu, S. -D, 2014. Evaluation of triple integrals, American Journal of Systems and Software, 2(4), 85-88.
  36. Apostol, T. M., 1975. Mathematical Analysis, 2nd ed., Massachusetts: Addison-Wesley.

Downloads

Published

2016-02-25

Issue

Section

Research Articles

How to Cite

[1]
Chii-Huei Yu, " Integral Problems of Trigonometric Functions, International Journal of Scientific Research in Science and Technology(IJSRST), Online ISSN : 2395-602X, Print ISSN : 2395-6011, Volume 2, Issue 1, pp.63-67, January-February-2016.