integral

C1 CET-6 Oxf 5000 大学 FREQ #21981 ★☆☆☆☆

n. 整体, 积分, 整数 a. 固有的, 整体的, 整数的, 积分的 [计] 积分

发音

UK /ˈɪntɪɡɹ(ə)l/
UK /ˈɪntɪɡr(ə)l/
US /ˈɪntəɡɹəl/
UK /ɪnˈtɛɡr(ə)l/
US /ɪnˈtɛɡɹəl/

词形变化

integrals 复数 integrals more integral 比较级 most integral 最高级

教材释义与例句

名词

积分；部分；完整

形容词

积分的；完整的，整体的；构成整体所必须的

释义与例句

n.
  1. 1.

    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.

    积分

    数学

    The integral of a univariate real-valued function is the area under its curve; but be warned! Not all functions are integrable!

  2. 2.

    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.

    Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.

    数学
  3. 3.

    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 the integrand (or, generally, differential form) appearing in front of the integral sign.

    数学

    Stokes' theorem relates the integral over a surface of the curl of a vector field to a line integral around the boundary of that surface: #92;int#95;S#92;nabla#92;times#92;mathbf#123;F#125;#92;cdotd#92;mathbf#123;S#125;#61;#92;int#95;#123;#92;partialS#125;#92;mathbf#123;F#125;#92;cdotd#92;mathbf#123;r#125;,.

  4. 4.

    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;

    数学

    The integral of x² is #92;frac#123;x³#125;#123;3#125; plus a constant.

  5. 5.

    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;

    The fluent of a given fluxion in Newtonian calculus.

    历史 废旧 数学
adj. C1 Oxf 5000
  1. 1.

    Constituting a whole together with other parts or factors; not omittable or removable.

    完整的

    完整嘅

  2. 2.

    Of, pertaining to, or being an integer.

    数学
  3. 3.

    Relating to integration (“the process of finding the integral [noun] of a function”).

    数学
  4. 4.

    Being the root of some monic polynomial in A.

    数学
  5. 5.

    Whole; undamaged.

    废旧

词汇关系

名词

上位词 4

figuring reckoning calculation computation

下位词 2

definite integral indefinite integral
形容词

同义词 6

entire intact constitutional built-in inherent inbuilt

近义相关 3

whole intrinsic intrinsical

相关短语

integral calculus [计] 积分学 integral equation [计] 积分方程 integral function [计] 整函数 integral domain [数]整环 integral functions integral equations integral membrane protein integral membrane proteins integral transform integral transforms integral domains integral element integral elements integral number [计] 整数

词源

Borrowed from Middle French integral, from Medieval Latin integrālis, from Latin integer (“entire”); see integer.

来源：wiktionary