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integral

From Wiktionary, the free dictionary
See also:INTEGRAL,Integral,intégral,andintegrál

English

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Etymology

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Borrowed fromMiddle Frenchintegral, fromMedieval Latinintegrālis, fromLatininteger(entire); seeinteger.

Pronunciation

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  • Noun
  • (UK)enPR:ĭnʹtĭ-grəl,IPA(key): /ˈɪntɪɡɹ(ə)l/
  • (US)enPR:ĭnʹtə-grəl,IPA(key): /ˈɪntəɡɹəl/,/ɪnˈtɛɡɹəl/
  • Audio(UK):(file)
  • Adjective
  • (UK)IPA(key): /ˈɪntɪɡr(ə)l/,/ɪnˈtɛɡr(ə)l/
  • (US)enPR:ĭn-tĕgʹrəl,IPA(key): /ˈɪntəɡɹəl/,/ɪnˈtɛɡɹəl/
  • Audio(UK):(file)

Adjective

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integral (comparativemoreintegral,superlativemostintegral)

  1. Constituting awhole together with otherparts orfactors; notomittable orremovable
    Synonyms:immanent,inherent,necessary;see alsoThesaurus:intrinsic
    • 1692–1717,Robert South,Twelve Sermons Preached upon Several Occasions, volume(please specify |volume=I to VI), London:
      Ceasing to do evil, and doing good, are the two greatintegral parts that complete this duty.
  2. (mathematics) Of, pertaining to, or being aninteger.
  3. (mathematics) Relating tointegration(the process of finding theintegral [noun] of afunction).
  4. (algebra, commutative algebra, of aringelement in aringB{\displaystyle B} relative to asubringA{\displaystyle A}) Being theroot of somemonicpolynomial inA{\displaystyle A}.
    Coordinate terms:integral element,algebraic
  5. (obsolete)Whole;undamaged.
    • 1627 (indicated as1626),Francis [Bacon], “(please specify the page, or |century=I to X)”, inSylua Syluarum: Or A Naturall Historie. In Ten Centuries. [], London: [] William Rawley [];[p]rinted by J[ohn] H[aviland] for William Lee [],→OCLC:
      A local motion keepeth bodiesintegral.

Derived terms

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Related terms

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Translations

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constituting a whole together with other parts or factors; not omittable or removable
math: of, pertaining to, or being an integer
math: relating to integration
The translations below need to be checked and inserted above into the appropriate translation tables. See instructions atWiktionary:Entry layout § Translations.
Translations to be checked

Noun

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EnglishWikipedia has an article on:
Wikipedia

integral (pluralintegrals)

  1. (mathematics) One of the two fundamentaloperations ofcalculus (the other beingdifferentiation), whereby afunction'sdisplacement,area,volume, or other qualities arising from the study ofinfinitesimal change are quantified, usually defined as alimiting process on asequence ofpartial sums. Denoted using along s:, or a variant thereof.
    Theintegral of aunivariatereal-valued function is the area under its curve; but be warned! Not all functions areintegrable!
    1. (specifically) Any of severalanalyticformalizations of this operation: theRiemann integral, theLebesgue integral, etc.
  2. (mathematics) Adefinite integral: the result of theapplication of such an operation onto a function and a suitablesubset of the function'sdomain: either anumber orpositive ornegativeinfinity. In the former case, the integral is said to befinite or toconverge; in the latter, the integral is said todiverge. In notation, the domain of integration is indicated either below the sign, or, if it is aninterval, with its endpoints as sub- and super-scripts, and the function being integrated forming part of theintegrand (or, generally,differential form) appearing in front of the integral sign.
    Stokes' theorem relates theintegral over a surface of thecurl of avector field to alineintegral around the boundary of that surface:S×FdS=SFdr,{\displaystyle \int _{S}\nabla \times \mathbf {F} \cdot d\mathbf {S} =\int _{\partial S}\mathbf {F} \cdot d\mathbf {r} ,}.
  3. (mathematics) Anindefinite integral: the result of the application of such an operation onto a function together with anindefinite domain, yielding a function; a function'santiderivative;
    Synonyms:antiderivative,indefinite integral,
    Antonym:derivative
    Theintegral ofx2{\displaystyle x^{2}} isx33{\displaystyle {\frac {x^{3}}{3}}} plus a constant.
    1. (mathematics, historical or obsolete) Thefluent of a givenfluxion inNewtonian calculus.

Derived terms

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Related terms

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Translations

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limit of sums
antiderivativeseeantiderivative

Anagrams

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Albanian

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Noun

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integral m

  1. (mathematics)integral (relating tointegration)

Further reading

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  • integral”, inFGJSH: Fjalor i gjuhës shqipe [Dictionary of the Albanian language] (in Albanian),2006
  • FGJSSH: Fjalor i gjuhës së sotme shqipe [Dictionary of the modern Albanian language]‎[1],1980

Catalan

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Etymology

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Borrowed fromMedieval Latinintegrālis, fromLatininteger.

Pronunciation

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Adjective

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integral m orf (masculine and feminine pluralintegrals)

  1. integral
  2. (of bread, etc.)wholegrain,wholemeal

Related terms

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Noun

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integral f (pluralintegrals)

  1. (mathematics)integral

Derived terms

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Further reading

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Indonesian

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Etymology

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Borrowed fromDutchintegraal(integral), fromFrenchintégral, fromMedieval Latinintegrālis, fromLatininteger(entire).

Pronunciation

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Adjective

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intêgral

  1. integral:
    1. constituting a whole together with other parts or factors; not omittable or removable
      Synonyms:bulat,utuh,sempurna
    2. (mathematics) relating to integration (“the process of finding the integral [noun] of a function”)

Noun

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intêgral (pluralintegral-integral)

  1. (mathematics)integral

Related terms

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Further reading

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Middle French

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Etymology

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Borrowed fromMedieval Latinintegrālis, fromLatininteger.

Adjective

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integral m (feminine singularintegrale,masculine pluralintegraux,feminine pluralintegrales)

  1. integral, necessary to the function of the whole
  2. whole;entire

Descendants

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References

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  • integral onDictionnaire du Moyen Français (1330–1500) (in French)

Portuguese

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Etymology

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Borrowed fromMedieval Latinintegrālis, fromLatininteger(entire; untouched).

Pronunciation

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  • (Portugal)IPA(key): /ĩ.tɨˈɡɾal/[ĩ.tɨˈɣɾaɫ]
    • (Southern Portugal)IPA(key): /ĩ.tɨˈɡɾa.li/[ĩ.tɨˈɣɾa.li]

  • Rhymes:-al,-aw
  • Hyphenation:in‧te‧gral

Adjective

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integral m orf (pluralintegrais)

  1. integral;whole;entire
  2. (of food)whole(from which none of its constituents has been removed)

Quotations

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For quotations using this term, seeCitations:integral.

Synonyms

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Derived terms

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Noun

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integral f orm (pluralintegrais)

  1. (mathematics)integral(limits of sums)
  2. (mathematics)antiderivative
    Synonym:antiderivada

Quotations

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For quotations using this term, seeCitations:integral.

Related terms

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Further reading

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Romanian

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Etymology

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Borrowed fromFrenchintégral,Medieval Latinintegrālis.

Pronunciation

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Adjective

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integral m orn (feminine singularintegrală,masculine pluralintegrali,feminine and neuter pluralintegrale)

  1. integral
    Synonyms:întreg,complet

Declension

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Declension ofintegral
singularplural
masculineneuterfemininemasculineneuterfeminine
nominative-
accusative
indefiniteintegralintegralăintegraliintegrale
definiteintegralulintegralaintegraliiintegralele
genitive-
dative
indefiniteintegralintegraleintegraliintegrale
definiteintegraluluiintegraleiintegralilorintegralelor

Related terms

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Spanish

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Etymology

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Borrowed fromMedieval Latinintegrālis, fromLatininteger(entire).

Pronunciation

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  • IPA(key): /inteˈɡɾal/[ĩn̪.t̪eˈɣ̞ɾal]
  • Audio(Colombia):(file)
  • Rhymes:-al
  • Syllabification:in‧te‧gral

Adjective

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integral m orf (masculine and feminine pluralintegrales)

  1. integral
  2. whole
  3. brown(rice)
  4. wholegrain

Derived terms

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Related terms

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Noun

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integral f (pluralintegrales)

  1. (mathematics)integral

Further reading

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Swedish

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SwedishWikipedia has an article on:
Wikipediasv

Etymology

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(Thisetymology is missing or incomplete. Please add to it, or discuss it at theEtymology scriptorium.)

Pronunciation

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  • IPA(key): /ɪntɛˈɡrɑːl/
  • Hyphenation:in‧te‧gral
  • Rhymes:-ɑːl

Noun

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integral c

  1. (mathematics) anintegral

Declension

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Declension ofintegral
nominativegenitive
singularindefiniteintegralintegrals
definiteintegralenintegralens
pluralindefiniteintegralerintegralers
definiteintegralernaintegralernas

Related terms

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References

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Anagrams

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Tagalog

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Etymology

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Borrowed fromSpanishintegral.

Pronunciation

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Adjective

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integrál (Baybayin spellingᜁᜈ᜔ᜆᜒᜄ᜔ᜇᜎ᜔)

  1. integral
    Synonyms:buo,kompleto

Related terms

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Turkish

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Etymology

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Borrowed fromFrenchintégral.

Pronunciation

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Noun

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integral (definite accusativeintegrali,pluralintegraller)

  1. (mathematics)integral
    abf(x)dx{\displaystyle \int _{a}^{b}\!f(x)\,dx\,}

Declension

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Declension ofintegral
Possessive forms
nominative
singularplural
1st singularintegralimintegrallerim
2nd singularintegralinintegrallerin
3rd singularintegraliintegralleri
1st pluralintegralimizintegrallerimiz
2nd pluralintegralinizintegralleriniz
3rd pluralintegralleriintegralleri
definite accusative
singularplural
1st singularintegralimiintegrallerimi
2nd singularintegraliniintegrallerini
3rd singularintegraliniintegrallerini
1st pluralintegralimiziintegrallerimizi
2nd pluralintegraliniziintegrallerinizi
3rd pluralintegralleriniintegrallerini
dative
singularplural
1st singularintegralimeintegrallerime
2nd singularintegralineintegrallerine
3rd singularintegralineintegrallerine
1st pluralintegralimizeintegrallerimize
2nd pluralintegralinizeintegrallerinize
3rd pluralintegrallerineintegrallerine
locative
singularplural
1st singularintegralimdeintegrallerimde
2nd singularintegralindeintegrallerinde
3rd singularintegralindeintegrallerinde
1st pluralintegralimizdeintegrallerimizde
2nd pluralintegralinizdeintegrallerinizde
3rd pluralintegrallerindeintegrallerinde
ablative
singularplural
1st singularintegralimdenintegrallerimden
2nd singularintegralindenintegrallerinden
3rd singularintegralindenintegrallerinden
1st pluralintegralimizdenintegrallerimizden
2nd pluralintegralinizdenintegrallerinizden
3rd pluralintegrallerindenintegrallerinden
genitive
singularplural
1st singularintegraliminintegrallerimin
2nd singularintegralininintegrallerinin
3rd singularintegralininintegrallerinin
1st pluralintegralimizinintegrallerimizin
2nd pluralintegralinizinintegrallerinizin
3rd pluralintegrallerininintegrallerinin
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