integral

微积分的两个基本运算之一(另一个是微分),通过极限过程对部分和序列求和来量化函数的位移、面积、体积等由无穷小变化引起的性质,记作长s:∫或其变体。

One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a long s: ∫, or a variant thereof.

定积分:对函数及其定义域的合适子集施以此运算的结果,要么是数,要么是正负无穷。前者称积分有限或收敛,后者称发散。在记号中,积分域标在积分号下方,若是区间则以端点作上下标,被积函数构成......

A definite integral: the result of the application of such an operation onto a function and a suitable subset of the function's domain: either a number or positive or negative infinity. In the former case, the integral is said to be finite or to converge; in the latter, the integral is said to diverge. In notation, the domain of integration is indicated either below the sign, or, if it is an interval, with its endpoints as sub- and super-scripts, and the function being integrated forming part of

不定积分:对函数施以此运算并带不定域,得到一个函数；即函数的反导数。

An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;