1. Expression: In high school mathematics, definite integral is introduced in the form of sum sign, which means that the area under the curve is approximately divided into infinite rectangles, and the areas of these rectangles are summed. In college mathematics, definite integral is introduced through the concept of limit, and the approximate sum of the area under the curve is gradually subdivided into infinitesimal rectangles, and then the areas of these rectangles are summed by limit operation.
2. Theoretical basis: The theoretical basis of the introduction of definite integral in university is more rigorous and in-depth. Based on the limit theory and the completeness of real numbers, it is defined and deduced by using the concepts of infinitesimal and limit. However, the introduction of high school definite integral is simplified, mainly focusing on the approximate solution of geometric figure area.
3. Integral symbol: In high school mathematics, definite integral is usually represented by ∫ symbol. In college mathematics, a more detailed symbol system is introduced. For example, ∫f(x)dx represents the definite integral of function f(x), where dx represents the infinitesimal change of independent variable x.
Definite integral is an important concept of calculus and has a wide range of applications. It can be used not only to calculate the area under the curve, but also to solve the arc length, mass and center of gravity of the curve. In engineering, physics, economy and other fields, definite integral is widely used in modeling and solving practical problems.