Regardless of the limit or derivative, the constant coefficient of each term can be proposed. The essence of integral is summation. If the sum has a common factor, you can first increase the common factor, sum the rest, and then multiply it by this constant. For a given positive real function, the definite integral in the real number interval can be understood as the area value of a curved trapezoid surrounded by curves, lines and axes on the coordinate plane.

definite integral

Here, we should pay attention to the relationship between definite integral and indefinite integral: if definite integral exists, it is a concrete numerical value, while indefinite integral is a functional expression, and they have only one mathematical relationship (Newton-Leibniz formula).

A function can have indefinite integral, but not definite integral; There can also be definite integral, but there is no indefinite integral. A continuous function must have definite integral and indefinite integral; If there are only a finite number of discontinuous points, the definite integral exists; If there is jump discontinuity, the original function must not exist, that is, the indefinite integral must not exist.