Solving Some Definite Integrals by Using Maple

Chii-Huei Yu

doi:10.13189/wjcat.2014.020301

Abstract

This study uses the mathematical software Maple for the auxiliary tool to evaluate two types of definite integrals. We can obtain the closed forms of these two types of definite integrals by using differentiation with respect to a parameter and Leibniz differential rule. 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.

Highlights

As information technology advances, whether computers can become comparable with human brains to perform abstract tasks, such as abstract art similar to the paintings of Picasso and musical compositions similar to those of Beethoven, is a natural question
This study introduces how to conduct mathematical research using the mathematical software Maple
We can obtain the closed forms of these two types of definite integrals by using differentiation with respect to a parameter and Leibniz differential rule ; these are the main results of this paper (i.e., Theorems 1, 2)

Summary

Introduction

Whether computers can become comparable with human brains to perform abstract tasks, such as abstract art similar to the paintings of Picasso and musical compositions similar to those of Beethoven, is a natural question. Even when Maple cannot determine the solution, problem-solving hints can be identified and inferred from the approximate values calculated and solutions to similar problems, as determined by Maple For this reason, Maple can provide insights into scientific research. This type of research method allows the discovery of calculation errors, and helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding problem-solving methods

Main Results

Theorem 1

Theorem 2

Examples

Example 1

Conclusion

Example 4