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一、定积分的定义一般地,设函数f(X)在区间[a,b]上有定义,将区间[a,b]等分成n个小区间,每个小区间的长度为Δx (Δ=(b-a)/n),在每个小区间上取一点x_i,依次为x_1,x_2,…,x_n.作和S_n=f(x_1)Δx+f(x_2)Δx+…+f(x_n)Δx =∑~n_(i=1)f(x_i)Δx,如果Δx无限趋近于0(亦即n趋向于+∞)时,S_n无限趋近于常数S,那么称该常数S为函数f(x)在区间[a,b]上的定积分(definiteintegral),记为S =∫_a~bf(x)dx,其中f(x)称为被积函数,[a,b]称为积分区间,a称为积分下限,b称为积分上限.
1. Definition of Definite Integral In general, let function f(X) be defined in the interval [a, b] and divide the interval [a, b] into n cells. The length between each cell is Δx (Δ =(ba)/n), taking a point x_i between each cell, followed by x_1,x_2,...,x_n. and S_n=f(x_1)Δx+f(x_2)Δx+...+f(x_n)Δx =∑~n_(i=1)f(x_i)Δx, if Δx infinitely approaches 0 (that is, n tends to +∞), S_n infinitely approaches a constant S, then the constant S is called a function f ( x) Definite integral over the interval [a, b], denoted as S = ∫ _a b bf(x)dx, where f(x) is called integrand and [a, b] is called integral interval ,a is called the lower limit of integration and b is called the upper limit of integration.