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, 6th edition, volumes (please specify |volume=I to VI), London: […] J[ames] Bettenham, for Jonah Bowyer, […], published 1727, →OCLC:

     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.
   • 1631, Francis [Bacon], “(please specify |century=I to X)”, in Sylua Syluarum: Or A Naturall Historie. In Ten Centuries. […], 3rd edition, London: […] William Rawley; [p]rinted by J[ohn] H[aviland] for William Lee […], →OCLC:

     A local motion keepeth bodies integral.

• integer
• integrity
• integrous (very rare)

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.

• integer

• 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]‎ (in Albanian), 1980

Borrowed from Medieval Latin integrālis, from Latin integer.

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

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, Vigésima tercera edición, Real Academia Española, 2014

(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/ [ʔɪn.tɛɡˈɾal]
• Rhymes: -al
• Syllabification: in‧teg‧ral

integrál (Baybayin spelling ᜁᜈ᜔ᜆᜒᜄ᜔ᜇᜎ᜔)

1. integral

   Synonyms: buo, kompleto

• integrasyon
• integrante

Borrowed from French intégral.

• IPA^(key): [in.tɛɟ.ˈɾalʲ]

integral (definite accusative integrali, plural integraller)

1. (mathematics) integral

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