Integration and Its Applications on Integral, Limit, and Beyond

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.