Integration is the inverse operation of differentiation, that is, knowing the derivative function of a function and finding the original function in reverse. In application, the function of integration is not only this, but also widely used in summation, that is, to find the area of curved triangle. This ingenious solution is determined by the special properties of integral.

Mainly divided into definite integral, indefinite integral and other integral. The properties of integral mainly include linearity, sign preservation, maximum and minimum, absolute continuity, absolute value integral and so on.

The definite integral of extended data is a kind of integral, which is the limit of the integral sum of function f(x) in the interval [a, b].

Here, we should pay attention to the relationship between definite integral and indefinite integral: definite integral, if it exists, is a specific numerical value (the area of curved trapezoid), while indefinite integral is a functional expression, and there is only one mathematical calculation relationship between them (Newton-Leibniz formula), and nothing else.

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.

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