integral

See also: INTEGRAL, Integral, intégral, and integrál

English

Etymology

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

Pronunciation

• 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

integral (comparative more integral, superlative most integral)

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

   Synonyms: immanent, inherent, necessary; see also Thesaurus: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 great integral parts that complete this duty.

2. (mathematics) Of, pertaining to, or being an integer.
3. (mathematics) Relating to integration (“the process of finding the integral [noun] of a function”).
4. (algebra, commutative algebra, of a ring element in a ring ${\displaystyle B}$ relative to a subring ${\displaystyle A}$) Being the root of some monic polynomial in ${\displaystyle A}$.

   Coordinate terms: integral element, algebraic

5. (obsolete) Whole; undamaged.
   • 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:

     A local motion keepeth bodies integral.

Derived terms

• 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

Related terms

• integer
• integrity
• integrous (very rare)

Translations

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

Bashkir: айырылғыһыҙ (ayırılğıhıź) Bulgarian: неразделен (bg) (nerazdelen), цялостен (bg) (cjalosten) Chinese: Cantonese: 完整嘅 (jyun4 zing2 ge3) Mandarin: 完整的 (wánzhěng de) Czech: nedílný Dutch: integraal (nl) Esperanto: integra (eo) Finnish: olennainen (fi), kokonaisuuteen kuuluva Galician: integral m or f German: integral (de), ein Ganzes ausmachend, zur Erhaltung des Ganzen unentbehrlich (descriptive) Greek: αναπόσπαστος (el) (anapóspastos) Hebrew: אִינְטֶגְרָלִי (he) (integráli) Hindi: समाकलन m (samāklan) Kazakh: интегралды (integraldy), интегралдық (integraldyq) Khmer: ដែលទាំងស្រុង (dael teang srong) Manx: slane Persian: please add this translation if you can Polish: jednolity (pl), integralny (pl) Portuguese: integral (pt) Romanian: integral (ro) Russian: неотъе́млемый (ru) (neotʺjémlemyj), недели́мый (ru) (nedelímyj), неотдели́мый (ru) (neotdelímyj) Swedish: hel (sv), enhetlig (sv)

math: of, pertaining to, or being an integer

Arabic: تَكَامُل (ar) m (takāmul) Bashkir: бөтөн һанлы (bötön hanlı) Bulgarian: целочислен (celočislen) Czech: celočíselný Dutch: geheel (nl) Esperanto: entjera Finnish: kokonaisluku- (fi) French: intégral (fr) German: ganzzahlig (de) Greek: ακέραιος (el) m (akéraios) Hindi: समाकलन m (samāklan) Kazakh: интегралды (integraldy), интегралдық (integraldyq) Manx: slane-earrooagh Portuguese: inteiro (pt) Romanian: integral (ro) Russian: целочи́сленный (ru) (celočíslennyj) Spanish: entero (es) Swedish: compounds with heltal (sv) Tagalog: buumbilangin

math: relating to integration

Bulgarian: интегрален (bg) (integralen) Esperanto: integrala Finnish: integraali- (fi) French: intégral (fr) Galician: integral Hindi: समाकलन m (samāklan) Kazakh: интегралды (integraldy), интегралдық (integraldyq) Spanish: integral (es)

The translations below need to be checked and inserted above into the appropriate translation tables. See instructions at Wiktionary:Entry layout § Translations.

Translations to be checked

Hungarian: (please verify) integrál (hu) (2) Manx: (please verify) co-hymagh

Noun

English Wikipedia has an article on:

integral

Wikipedia

integral (plural integrals)

1. (mathematics) 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!

   1. (specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.
2. (mathematics) 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 ${\displaystyle {\frac {1}{x}}}$ on ${\displaystyle [{\frac {1}{2}},1]}$ is ${\displaystyle \ln(2)}$, but the integral of the same function on ${\displaystyle (0,1]}$ diverges. In notation, ${\displaystyle \int _{\frac {1}{2}}^{1}{\frac {1}{x}}dx=\ln(2)}$, but ${\displaystyle \int _{0}^{1}{\frac {1}{x}}dx=\infty }$.

   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: ${\displaystyle \int _{S}\nabla \times \mathbf {F} \cdot d\mathbf {S} =\int _{\partial S}\mathbf {F} \cdot d\mathbf {r} ,}$.

3. (mathematics) 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;

   Synonyms: antiderivative, indefinite integral, ∫

   Antonym: derivative

   The integral of ${\displaystyle x^{2}}$ is ${\displaystyle {\frac {x^{3}}{3}}}$ plus a constant.

   1. (mathematics, historical or obsolete) The fluent of a given fluxion in Newtonian calculus.

Derived terms

• 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

Related terms

• integer

Translations

limit of sums

Armenian: ինտեգրալ (hy) (integral) Belarusian: інтэгра́л m (intehrál) Bulgarian: интегра́л m (integrál) Catalan: integració (ca) f Chinese: Cantonese: 積分 / 积分 (zik1 fan1) Hakka: chit-fûn-ho̍k Mandarin: 積分 / 积分 (zh) (jī fēn) Czech: integrál (cs) m Dutch: integraal (nl) Esperanto: integralo (eo), integro Finnish: integraali (fi) French: intégrale (fr) f Galician: integral f Georgian: ინტეგრალი (inṭegrali) German: Integral (de) n Greek: ολοκλήρωμα (el) n (oloklíroma) Hebrew: אִינְטֶגְרָל (he) m (integrál), אַסְכֶּמֶת (he) f (askémet) (Academy of the Hebrew Language) Hungarian: integrál (hu) Icelandic: heildun f, tegrun f Italian: integrale (it) m Japanese: 積分 (ja) (せきぶん, sekibun) Kazakh: интеграл (integral) Khmer: អាំងតេក្រាល (km) (ʼangteekraal) Korean: 적분 (ko) (jeokbun) Kyrgyz: интеграл (integral) Malay: kamiran Manx: co-hym m Mongolian: интеграл (mn) (integral) Norwegian: integral n Polish: całka (pl) f, całka oznaczona (pl) f Portuguese: integral (pt) f Romanian: integrală (ro) f Russian: интегра́л (ru) m (intɛgrál) Serbo-Croatian: Cyrillic: интѐгра̄л m Roman: intègrāl (sh) m Spanish: integral (es) f Sundanese: integral Swedish: integral (sv) c Tagalog: lagom Thai: ปริพันธ์ (bpà-rí-pan) Turkish: integral (tr) Ukrainian: інтегра́л (uk) m (intehrál) Vietnamese: tích phân (vi)

antiderivative — see antiderivative

Anagrams

• Triangle, alerting, altering, relating, tanglier, teraglin, triangle

Albanian

Noun

integral m

1. (mathematics) integral (relating to integration)

Further reading

• “integral”, in FGJSH: 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]‎, 1980

Catalan

Etymology

Borrowed from Medieval Latin integrālis, from Latin integer.

Pronunciation

• IPA^(key): (Central, Balearic) [in.təˈɣɾal]
• IPA^(key): (Valencia) [in.teˈɣɾal]

• Audio (Barcelona):

  (file)

Adjective

integral m or f (masculine and feminine plural integrals)

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

Related terms

• enter
• integració
• integrar
• íntegre

Noun

integral f (plural integrals)

1. (mathematics) integral

Derived terms

• integral indefinida

Further reading

• “integral”, in Diccionari de la llengua catalana [Dictionary of the Catalan Language] (in Catalan), second edition, Institute of Catalan Studies [Catalan: Institut d'Estudis Catalans], April 2007

Indonesian

Etymology

Borrowed from Dutch integraal (“integral”), from French intégral, from Medieval Latin integrālis, from Latin integer (“entire”).

Pronunciation

• (Standard Indonesian) IPA^(key): /intəɡˈral/ [in̪.t̪ək̚ˈral]
• Rhymes: -al
• Syllabification: in‧teg‧ral

Adjective

intêgral (comparative lebih integral, superlative paling integral)

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

intêgral (plural integral-integral)

1. (mathematics) integral

Related terms

• integrasi

Further reading

• “integral” in Kamus Besar Bahasa Indonesia, Jakarta: Agency for Language Development and Cultivation – Ministry of Education, Culture, Research, and Technology of the Republic of Indonesia, 2016.

Middle French

Etymology

Borrowed from Medieval Latin integrālis, from Latin integer.

Adjective

integral m (feminine singular integrale, masculine plural integraux, feminine plural integrales)

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

Descendants

• French: intégral

References

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

Portuguese

Etymology

Borrowed from Medieval Latin integrālis, from Latin integer (“entire; untouched”).

Pronunciation

• (Brazil) IPA^(key): /ĩ.teˈɡɾaw/ [ĩ.teˈɡɾaʊ̯]

 

• (Portugal) IPA^(key): /ĩ.tɨˈɡɾal/ [ĩ.tɨˈɣɾaɫ]

• (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

integral m or f (plural integrais)

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

Quotations

For quotations using this term, see Citations:integral.

Synonyms

• (whole): completo, íntegro, inteiro, intacto, total

Derived terms

• integralmente

Noun

integral f or m (plural integrais)

1. (mathematics) integral (limits of sums)
2. (mathematics) antiderivative

   Synonym: antiderivada

Quotations

For quotations using this term, see Citations:integral.

Related terms

• integrado
• integrar
• íntegro

Further reading

• “integral”, in Dicionário Priberam da Língua Portuguesa (in Portuguese), Lisbon: Priberam, 2008–2025

Romanian

Etymology

Borrowed from French intégral, Medieval Latin integrālis.

Pronunciation

• IPA^(key): /in.teˈɡral/

Adjective

integral m or n (feminine singular integrală, masculine plural integrali, feminine and neuter plural integrale)

1. integral

   Synonyms: întreg, complet

Declension

Declension of integral

		singular				plural
		masculine	neuter	feminine		masculine	neuter	feminine
nominative- accusative	indefinite	integral		integrală		integrali	integrale
	definite	integralul		integrala		integralii	integralele
genitive- dative	indefinite	integral		integrale		integrali	integrale
	definite	integralului		integralei		integralilor	integralelor

Related terms

• integru

Spanish

Etymology

Borrowed from Medieval Latin integrālis, from Latin integer (“entire”).

Pronunciation

• IPA^(key): /inteˈɡɾal/ [ĩn̪.t̪eˈɣ̞ɾal]

• Audio (Colombia):

  (file)

• Rhymes: -al
• Syllabification: in‧te‧gral

Adjective

integral m or f (masculine and feminine plural integrales)

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

Derived terms

• arroz integral
• cálculo integral
• integralidad
• integralmente
• pan integral
• parte integral

Related terms

• íntegro

Noun

integral f (plural integrales)

1. (mathematics) integral

Further reading

• “integral”, in Diccionario de la lengua española [Dictionary of the Spanish Language] (in Spanish), online version 23.8, Royal Spanish Academy [Spanish: Real Academia Española], 10 December 2024

Swedish

Swedish Wikipedia has an article on:

integral

Wikipedia ^sv

Etymology

(This etymology is missing or incomplete. Please add to it, or discuss it at the Etymology scriptorium.)

Pronunciation

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

Noun

integral c

1. (mathematics) an integral

Declension

Declension of integral

		nominative	genitive
singular	indefinite	integral	integrals
	definite	integralen	integralens
plural	indefinite	integraler	integralers
	definite	integralerna	integralernas

Related terms

• integrand
• integration
• integrera

References

• integral in Svensk ordbok (SO)
• integral in Svenska Akademiens ordlista (SAOL)
• integral in Svenska Akademiens ordbok (SAOB)

Anagrams

• triangel

Tagalog

Etymology

Borrowed from Spanish integral.

Pronunciation

• (Standard Tagalog) IPA^(key): /ʔinteɡˈɾal/ [ʔɪn̪.t̪ɛɡˈɾal]
• Rhymes: -al
• Syllabification: in‧teg‧ral

Adjective

integrál (Baybayin spelling ᜁᜈ᜔ᜆᜒᜄ᜔ᜇᜎ᜔)

1. integral

   Synonyms: buo, kompleto

Related terms

• integrante
• integrasyon

Turkish

Etymology

Borrowed from French intégral.

Pronunciation

• IPA^(key): [in.tɛɟ.ˈɾalʲ]

Noun

integral (definite accusative integrali, plural integraller)

1. (mathematics) integral

   ${\displaystyle \int _{a}^{b}\!f(x)\,dx\,}$

Declension

Declension of integral

singular plural nominative integral integraller definite accusative integrali integralleri dative integrale integrallere locative integralde integrallerde ablative integralden integrallerden genitive integralin integrallerin Possessive forms nominative singular plural 1st singular integralim integrallerim 2nd singular integralin integrallerin 3rd singular integrali integralleri 1st plural integralimiz integrallerimiz 2nd plural integraliniz integralleriniz 3rd plural integralleri integralleri definite accusative singular plural 1st singular integralimi integrallerimi 2nd singular integralini integrallerini 3rd singular integralini integrallerini 1st plural integralimizi integrallerimizi 2nd plural integralinizi integrallerinizi 3rd plural integrallerini integrallerini dative singular plural 1st singular integralime integrallerime 2nd singular integraline integrallerine 3rd singular integraline integrallerine 1st plural integralimize integrallerimize 2nd plural integralinize integrallerinize 3rd plural integrallerine integrallerine locative singular plural 1st singular integralimde integrallerimde 2nd singular integralinde integrallerinde 3rd singular integralinde integrallerinde 1st plural integralimizde integrallerimizde 2nd plural integralinizde integrallerinizde 3rd plural integrallerinde integrallerinde ablative singular plural 1st singular integralimden integrallerimden 2nd singular integralinden integrallerinden 3rd singular integralinden integrallerinden 1st plural integralimizden integrallerimizden 2nd plural integralinizden integrallerinizden 3rd plural integrallerinden integrallerinden genitive singular plural 1st singular integralimin integrallerimin 2nd singular integralinin integrallerinin 3rd singular integralinin integrallerinin 1st plural integralimizin integrallerimizin 2nd plural integralinizin integrallerinizin 3rd plural integrallerinin integrallerinin