integral

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

• 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)

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.

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;

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

   Synonyms: antiderivative, indefinite integral, ∫

   Antonym: derivative

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

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

integral m

1. (mathematics) integral (relating to integration)

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

Borrowed from Medieval Latin integrālis, from Latin integer.

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

integral m or f (masculine and feminine plural integrals)

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

integral f (plural integrals)

1. (mathematics) integral

• integral indefinida

• “integral” in Diccionari de la llengua catalana, segona edició, Institut d’Estudis Catalans.

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

• IPA^(key): /ɪn.tə.ˈɡral/
• Rhymes: -ɡral, -ral
• Hyphenation: in‧têg‧ral

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”).

intêgral (plural integral-integral, first-person possessive integralku, second-person possessive integralmu, third-person possessive integralnya)

1. (mathematics) integral

• “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.

Borrowed from Medieval Latin integrālis, from Latin integer.

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

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

• French: intégral

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

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

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

integral m or f (plural integrais)

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

For quotations using this term, see Citations:integral.

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

• integralmente

integral f or m (plural integrais)

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

   Synonym: antiderivada

For quotations using this term, see Citations:integral.

• “integral”, in Dicionário Priberam da Língua Portuguesa (in Portuguese), Lisbon: Priberam, 2008–2024

Borrowed from French intégral, Medieval Latin integrālis.

• IPA^(key): /in.teˈɡral/

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

1. integral

   Synonyms: întreg, complet

• integru

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

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

• Audio (Colombia):

  (file)

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

integral m or f (masculine and feminine plural integrales)

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

integral f (plural integrales)

1. (mathematics) integral

• “integral”, in Diccionario de la lengua española [Dictionary of the Spanish Language] (in Spanish), online version 23.7, Royal Spanish Academy [Spanish: Real Academia Española], 2023 November 28

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

• IPA^(key): /ɪntɛˈɡraːl/

integral c

1. (mathematics) an integral

• integrand
• integration
• integrera

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

• triangel

Borrowed from Spanish integral.

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

integrál (Baybayin spelling ᜁᜈ᜔ᜆᜒᜄ᜔ᜇᜎ᜔)

1. integral

   Synonyms: buo, kompleto

Borrowed from French intégral.

• IPA^(key): [in.tɛɟ.ˈɾalʲ]

integral (definite accusative integrali, plural integraller)

1. (mathematics) integral

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

Inflection
Nominative	integral
Definite accusative	integrali
	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