Mathematical definition: If the function f(x) is continuous on the interval [a, b], divide the interval [a, b] by n with the fraction xi? Between cells, take a little RI (I = 1, 2,3) [xi-1,xi] between each cell? ，n)？ And the formula f(r 1)+...+f(rn)? When n approaches infinity, the above sum approaches a constant A, which is called y=f(x)? Definite integral on interval.
Write /ab? f(x)？ dx？ Namely. /ab？ f(x)？ dx？ = limn & gt00? [f(r 1)+...+f(rn)]，？ Here, a? With what? B is called the lower integral limit and the upper integral limit, and the interval [a, b]? It's called the integral interval, the function f(x)? It's called integrand function, x? It's called an integral variable, f(x)dx? It is called the integrand function.
The formal name of definite integral is Riemann integral. In Riemann's own words, the image of a function in a rectangular coordinate system is divided into countless rectangles by a straight line parallel to the Y axis, and then the rectangles in a certain interval [a, b] are accumulated to get the image area of this function in the interval [a, b].