Application of Maple on Evaluation of Definite Integrals

Abstract:

This study uses the mathematical software Maple for the auxiliary tool to evaluate two types of definite integrals. We can determine the closed forms of these two types of definite integrals by using Leibniz differential rule and differentiation with respect to a parameter. At the same time, 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 by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. Therefore, Maple provides insights and guidance regarding problem-solving methods.

• Periodical: Applied Mechanics and Materials (Volumes 479-480)
• Pages: 823-827
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.479-480.823
• Online since: December 2013
• Authors: Chii Huei Yu
• Keywords: Closed Forms, Definite Integrals, Differentiation with Respect to a Parameter, Leibniz Differential Rule, MAPLE

References

[1] M.L. Abell and J.P. Braselton: Maple by Example, 3rd ed., Elsevier Academic Press (2005).

[2] J.S. Robertson: Engineering Mathematics with Maple, McGraw-Hill (1996).

[3] C. Tocci and S.G. Adams: Applied Maple for Engineers and Scientists, Artech House (1996).

[4] R.J. Stroeker and J.F. Kaashoek: Discovering Mathematics with Maple : An Interactive Exploration for Mathematicians, Engineers and Econometricians, Birkhauser Verlag (1999).

[5] C. -H. Yu: The Improper Integral Problems Related to Hyperbolic Functions, Tzu Hui Journal, Vol. 8 (2012), pp.192-203.

[6] C. -H. Yu: Application of Maple on Some Type of Improper Integral Problem, Workshop on Consumer Electronics, National Formosa University (2012), P0081.

[7] C. -H. Yu: Application of Maple on Solving the Improper Integral Problems, 2012 Digital and Technology Life on Innovative Applications Symposium, Taoyuan Innovation Institute of Technology (2012).

[8] C. -H. Yu: Application of Maple: Taking Two Special Integral Problems as Examples, The 8th International Conference on Knowledge Community, Chinese Culture University, Taiwan (2012), pp.803-811.

[9] C. -H. Yu: Application of Maple on Some Integral Problems, International Conference on Safety & Security Management and Engineering Technology 2012, WuFeng University, Taiwan (2012), pp.290-294.

[10] C. -H. Yu: Application of Maple on the Integral Problem of Some Type of Rational Functions, Annual Meeting and Academic Conference for Association of IE, 2012, Da-Yeh University, Taiwan (2012), D357-D362.

[11] C. -H. Yu: Application of Maple on Some Type of Integral Problem, Ubiquitous-Home Conference 2012, Kun Shan University, Taiwan (2012), pp.206-210.

[12] C. -H. Yu: Application of Maple on Evaluating the Closed Forms of Two Types of Integrals, The 17th Mobile Computing Workshop, Chang Gung University, Taiwan (2012), ID16.

[13] D.V. Widder: Advanced Calculus, 2nd ed., chapter, 10, Prentice-Hall (1961).

[14] L. Flatto: Advanced Calculus, The Williams & Wilkins (1976), p.405.

[15] T.M. Apostol: Mathematical Analysis, 2nd ed., Addison-Wesley (1975), p.121.