The definite integral is to find the bottom area of the graph line in the wave interval [a, b] by using the function f(X). That is, the area of the graph surrounded by y = 0, x = a, x = b and y = f (x). This figure is called a curved trapezoid, and the special case is a curved triangle.

Let the function f(x) be continuous on the interval [a, b], and divide the interval [a, b] into n subintervals [a, x0], (x0, x 1), (x 1, x2), ... (xi, b). You can know that the length of each interval is

In each subinterval (xi- 1, xi), take a little ξ i (i = 1, 2, …, n) as the summation formula (see the figure below), and let λ = max {△ x 1, △x2, …, △ xi}.

Where: a is called the lower integral limit, b is called the upper integral limit, the interval [a, b] is called the integral interval, the function f(x) is called the integrand, x is called the integrand symbol.

Extended data:

1, 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 function expression, and they have only one mathematical relationship (Newton-Leibniz formula).

2. 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.