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Words, grammatical forms and meanings linked to the ontology.

integral en · ADJ

Pronunciation

  • (US) audio
  • (UK) audio
  • /ɪnˈtɛɡr(ə)l/ (Received-Pronunciation)
  • ʹĭn-tə-grəl (General-American)
  • /ˈɪntəɡɹəl/ (General-American)
  • /ɪnˈtɛɡɹəl/ (General-American)
  • /ˈɪntɪɡr(ə)l/ (Received-Pronunciation)
  • ĭn-tĕgʹrəl (General-American)

Etymology

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

Meanings

  1. Constituting a whole together with other parts or factors; not omittable or removable.
    • When the verdict comes down, the transformation of the wunderkind founder of Theranos from black-clad genius to besuited milquetoast will be an integral part of the story. 2021 December 17, Vanessa Friedman, “The Verdict on the Elizabeth Holmes Trial Makeover”, in The New York Times, →ISSN, archived from the original on 12 Apr 2022:
    • Ceasing to do evil, and doing good, are the two great integral parts that complete this duty. 1692–1717, Robert South, Twelve Sermons Preached upon Several Occasions, volume (please specify |volume=I to VI), London:
  2. Of, pertaining to, or being an integer.
  3. Relating to integration (“the process of finding the integral [noun] of a function”).
  4. (of a ring element in a ring B relative to a subring A, qualifier:commutative algebra) Being the root of some monic polynomial in A.
  5. (obsolete) Whole; undamaged.
    • A local motion keepeth bodies integral. 1627 (indicated as 1626), Francis [Bacon], “(please specify the page, or |century=I to X)”, in Sylua Syluarum: Or A Naturall Historie. In Ten Centuries. […], London: […] William Rawley […]; [p]rinted by J[ohn] H[aviland] for William Lee […], →OCLC:

Forms

SpellingFeaturesLabelsSource
more integral Degree=Cmp lexicographic
most integral Degree=Sup lexicographic

Coordinates

algebraic · integral element

Deriveds

integral psychology · integrally · integral transformative practice · integral homology group · integral drawing · integral closure · integral energy · integral geometry · integral politics · integral yoga · integral element · integral polygedron · integral extension · integral ecology · integral curve · integral field unit · integralism · integral curvature · integral polynomial · nonintegral · integral function · integral cosmology · semi-integral · integral membrane protein · integral current · integrity · integral cuboid · integraph · integralist · integral post-metaphysics · integral number · integral fast reactor · unintegral · integral domain · integral brick · integralness · integral graph · differintegral · integrality · integral kernel

Relateds

integrous · integer · integrity

Synonyms

necessary · integral · ingrained · inherent · radical · immanent · inherent · resident · essential · inbuilt · inwrought · immanent · intrinsic · inborn · infused · built-in

Translations (62)

kk интегралдық (math: relating to integration) · el ακέραιος (math: of, pertaining to, or being an integer) · ro integral (constituting a whole together with other parts or factors; not omittable or removable) · es integral (constituting a whole together with other parts or factors; not omittable or removable) · fi olennainen (constituting a whole together with other parts or factors; not omittable or removable) · es entero (math: of, pertaining to, or being an integer) · gv slane (constituting a whole together with other parts or factors; not omittable or removable) · ru неотъе́млемый (constituting a whole together with other parts or factors; not omittable or removable) · fr entier (math: of, pertaining to, or being an integer) · eo integrala (math: relating to integration) · hi समाकलन (math: relating to integration) · pt inteiro (math: of, pertaining to, or being an integer) · hi समाकलन (constituting a whole together with other parts or factors; not omittable or removable) · cmn 完整的 (constituting a whole together with other parts or factors; not omittable or removable) · tl buumbilangin (math: of, pertaining to, or being an integer) · sv hel (constituting a whole together with other parts or factors; not omittable or removable) · hi समाकलन (math: of, pertaining to, or being an integer) · yue 完整嘅 (constituting a whole together with other parts or factors; not omittable or removable) · cs celočíselný (math: of, pertaining to, or being an integer) · eo integra (constituting a whole together with other parts or factors; not omittable or removable) · de integral (constituting a whole together with other parts or factors; not omittable or removable) · fi kokonaisuuteen kuuluva (constituting a whole together with other parts or factors; not omittable or removable) · km ដែលទាំងស្រុង (constituting a whole together with other parts or factors; not omittable or removable) · bg цялостен (constituting a whole together with other parts or factors; not omittable or removable) · de zur Erhaltung des Ganzen unentbehrlich (constituting a whole together with other parts or factors; not omittable or removable) · kk интегралдық (math: of, pertaining to, or being an integer) · gv slane-earrooagh (math: of, pertaining to, or being an integer) · sv enhetlig (constituting a whole together with other parts or factors; not omittable or removable) · bg целочислен (math: of, pertaining to, or being an integer) · de ganzzahlig (math: of, pertaining to, or being an integer) · kk интегралды (constituting a whole together with other parts or factors; not omittable or removable) · ar تَكَامُلِيّ (math: relating to integration) · kk интегралды (math: of, pertaining to, or being an integer) · de ein Ganzes ausmachend (constituting a whole together with other parts or factors; not omittable or removable) · bg неразделен (constituting a whole together with other parts or factors; not omittable or removable) · ro integral (math: of, pertaining to, or being an integer) · nl geheel (math: of, pertaining to, or being an integer) · eo entjera (math: of, pertaining to, or being an integer) · ru недели́мый (constituting a whole together with other parts or factors; not omittable or removable) · el αναπόσπαστος (constituting a whole together with other parts or factors; not omittable or removable) · pt integral (constituting a whole together with other parts or factors; not omittable or removable) · ba айырылғыһыҙ (constituting a whole together with other parts or factors; not omittable or removable) · sv compounds with heltal (math: of, pertaining to, or being an integer) · ru целочи́сленный (math: of, pertaining to, or being an integer) · ru неотдели́мый (constituting a whole together with other parts or factors; not omittable or removable) · es integral (math: relating to integration) · cs nedílný (constituting a whole together with other parts or factors; not omittable or removable) · pl jednolity (constituting a whole together with other parts or factors; not omittable or removable) · he אִינְטֶגְרָלִי (constituting a whole together with other parts or factors; not omittable or removable) · fr intégral (math: relating to integration) · fi kokonaisluku- (math: of, pertaining to, or being an integer) · fi integraali- (math: relating to integration) · ar صَحِيح (math: of, pertaining to, or being an integer) · kk интегралдық (constituting a whole together with other parts or factors; not omittable or removable) · gl integral (constituting a whole together with other parts or factors; not omittable or removable) · kk интегралды (math: relating to integration) · vi tích phân (math: relating to integration) · pl integralny (constituting a whole together with other parts or factors; not omittable or removable) · bg интегрален (math: relating to integration) · gl integral (math: relating to integration) · ba бөтөн һанлы (math: of, pertaining to, or being an integer) · nl integraal (constituting a whole together with other parts or factors; not omittable or removable)

integral en · NOUN

Pronunciation

  • (US) audio
  • (UK) audio
  • /ɪnˈtɛɡr(ə)l/ (Received-Pronunciation)
  • ʹĭn-tə-grəl (General-American)
  • /ˈɪntɪɡɹ(ə)l/ (UK)
  • /ˈɪntəɡɹəl/ (General-American)
  • /ˈɪntəɡɹəl/ (US)
  • /ɪnˈtɛɡɹəl/ (General-American)
  • (UK) audio
  • /ˈɪntɪɡr(ə)l/ (Received-Pronunciation)
  • /ɪnˈtɛɡɹəl/ (US)
  • ĭnʹtə-grəl (US)
  • ĭn-tĕgʹrəl (General-American)
  • ĭnʹtĭ-grəl (UK)

Etymology

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

Meanings

  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. (specifically) 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.
  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.
    • 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. 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. (historical, obsolete) 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.

Forms

SpellingFeaturesLabelsSource
integrals Number=Plur lexicographic

Antonyms

derivative · derivative

Deriveds

logarithmic integral · volume integral · ordered integral domain · Riemann-Stieltjes integral · Barnes integral · contour integral · Jackson integral · Sugeno integral · particular integral · integral transform · integration · Hellinger integral · improper integral · Volterra integral equation · Mellin-Barnes integral · double integral · indefinite integral · triple integral · flux integral · surface integral · iterated integral · integral theory · integral equation · path integral formalism · Choquet integral · Riemann integral · integral calculus · definite integral · half-integral · line integral · Lebesgue integral

Relateds

integer · integrate

Synonyms

mul:∫ · antiderivative · indefinite integral · indefinite integral · antiderivative · mul:∫

Translations (48)

is heildun (limit of sums) · nl integraal (limit of sums) · de Integral (limit of sums) · ca integració (limit of sums) · vi tích phân (limit of sums) · pl całka oznaczona (limit of sums) · be інтэгра́л (limit of sums) · es integral (limit of sums) · gv co-hym (limit of sums) · gl integral (limit of sums) · ms kamiran (limit of sums) · fi integraali (limit of sums) · ar تَكَامُل (limit of sums) · cs integrál (limit of sums) · he אַסְכֶּמֶת (limit of sums) · sv integral (limit of sums) · ru интегра́л (limit of sums) · su integral (limit of sums) · km អាំងតេក្រាល (limit of sums) · is tegrun (limit of sums) · th ปริพันธ์ (limit of sums) · cmn 積分 /积分 (limit of sums) · hu integrál (limit of sums) · hy ինտեգրալ (limit of sums) · tl lagom (limit of sums) · eo integralo (limit of sums) · sh intègrāl (limit of sums) · ko 적분 (limit of sums) · he אִינְטֶגְרָל (limit of sums) · pt integral (limit of sums) · ro integrală (limit of sums) · el ολοκλήρωμα (limit of sums) · pl całka (limit of sums) · mn интеграл (limit of sums) · yue 積分 /积分 (limit of sums) · kk интеграл (limit of sums) · it integrale (limit of sums) · eo integro (limit of sums) · hak chit-fûn-ho̍k (limit of sums) · uk інтегра́л (limit of sums) · sh интѐгра̄л (limit of sums) · bg интегра́л (limit of sums) · ja 積分 (limit of sums) · ka ინტეგრალი (limit of sums) · tr integral (limit of sums) · ky интеграл (limit of sums) · fr intégrale (limit of sums) · no integral (limit of sums)