# Integration and Its Applications on Integral, Limit, and Beyond

• Xinran Tian

## Keywords:

Real analysis; Definite integral; Limit; Fourier transformation.

## Abstract

The definite integral is a very important concept in real analysis and it has many applications in diverse disciplines. For example, the area under the curve can be calculated by cutting and approximating the curve, and the arc length of the curve and the volume of the rotating body can be solved by the definite integral. Therefore, definite integral has a wide range of applications in the field of science and engineering, such as circuits, mechanics, fluid mechanics, quantum mechanics. It also has application on other fields that will involve the operation of integral to promote the development of science, which makes it important for the whole science area. However, in the process of studying definite integrals, people will face many problems, such as insufficient theoretical support, lack of professional guidance, and insufficient timely summary in the research process. In order to solve these problems, researchers should correct their attitude towards scientific research, be realistic and down-to-earth. The purpose of this paper is to express the opinion on definite integral and hope to carry forward the great development of definite integral.

## Downloads

Download data is not yet available.

## References

James Ward Brown, Ruel V. Churchill, Complex Variables and Applications, 2014.

Liu Bingwen, Long Zhiwen. An example of unbounded function. Journal of Science of Teachers’ College and University, 2022, 42(4): 75-77.

Kalman D. Six ways to sum a series. College Math. J., 1993, 24: 402-421.

Ma Yanli. The Calculation of Definite Integral of Several Special Functions. Journal of Yuxi Normal University, 2021, 37(6): 22-28.

Serhan D. Students' Understanding of the Definite Integral Concept. International Journal of Research in Education and Science. 2015, 1(1): 84-88.

Zhao Xiaohui, Wei Wenying, Li Xiaomin, Yang Guangwu, Starting from Euler's formula. Technology Wind, 2023, 30(5): 13-15.

Jones S. R., Regions, Antiderivatives, and Addition: Definite integrals in Pure Mathematics and Applied Science Contexts. Journal of Mathematical Behavior, 2015, 38:9-28.

Liu Yongmei, Wang Guohui, Guan Yong, et al. Formal Vertification of Green’s theorem and Its Applications. Computer Engineering & Science, 2023, 45(07): 1178-1187.

Luo Fenghu. A Functional Proof of Euler’s Formula. Research in Middle School Mathematics (South China Normal University Edition), 2023, 14(3): 47.

Fang Xiande, Dai Qiumin. Modeling of turbine mass flow rate performances using the Taylor expansion. Applied Thermal Engineering, 2010, 30: 1824-1831.

29-03-2024

Articles

## How to Cite

Tian, X. (2024). Integration and Its Applications on Integral, Limit, and Beyond. Highlights in Science, Engineering and Technology, 88, 785-789. https://doi.org/10.54097/zansr122