integral

名词 n. 形容词 adj.
中文释义
英 /ˈɪntɪɡr(ə)l/|/ɪnˈtɛɡr(ə)l/    美 /ˈɪntəɡɹəl/|/ɪnˈtɛɡɹəl/

英文释义

名词 n.
  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.
    — The integral of a univariate real-valued function is the area under its curve; but be warned! Not all functions are integrable!
  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. specifically
  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.
    — The integral of #92;frac#123;1#125;#123;x#125; on #91;#92;frac#123;1#125;#123;2#125;,1#93; is #92;ln(2), but the integral of the same function on (0,1#93; diverges. In notation, #92;int#95;#92;frac#123;1#125;#123;2#125;¹#92;frac#123;1#125;#123;x#125;dx#61;#92;ln(2), but #92;int#95;0¹#92;frac#123;1#125;#123;x#125;dx#61;#92;infty.
  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;
    — The integral of x² is #92;frac#123;x³#125;#123;3#125; plus a constant.
  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. historical,obsolete
形容词 adj.
  1. Constituting a whole together with other parts or factors; not omittable or removable.
    — Ceasing to do evil, and doing good, are the two great integral parts that complete this duty.
  2. Of, pertaining to, or being an integer.
  3. Relating to integration (“the process of finding the integral [noun] of a function”).
  4. Being the root of some monic polynomial in A.
  5. Whole; undamaged. obsolete
    — A local motion keepeth bodies integral.

词形变化

more integral comparative most integral superlative integrals plural

词汇关系

衍生词
differintegral integral brick integral closure integral cosmology integral cuboid integral current integral curvature integral curve integral domain integral drawing integral ecology integral element integral energy integral extension integral fast reactor integral field unit integral function integral geometry integral graph integral homology group integralism integralist integrality integral kernel integrally integral membrane protein integralness integral number integral politics integral polygedron integral polynomial integral post-metaphysics integral psychology integral transformative practice integral yoga integraph integrity nonintegral semi-integral unintegral Barnes integral Choquet integral contour integral definite integral double integral flux integral half-integral Hellinger integral improper integral indefinite integral integral calculus integral equation integral theory integral transform integration iterated integral Jackson integral Lebesgue integral line integral logarithmic integral Mellin-Barnes integral ordered integral domain particular integral path integral formalism Riemann integral Riemann-Stieltjes integral Sugeno integral surface integral triple integral Volterra integral equation volume integral
相关词
integer integrity integrous integrate

词源

词源 1
Borrowed from Middle French integral, from Medieval Latin integrālis, from Latin integer (“entire”); see integer.
词源 2
Borrowed from Middle French integral, from Medieval Latin integrālis, from Latin integer (“entire”); see integer.
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