# integral
## English
### Etymology

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

### Pronunciation

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

### Adjective

integral (comparative more integral, superlative most integral)
* 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.
* (mathematics) Of, pertaining to, or being an integer.
* (mathematics) Relating to integration (“the process of finding the integral [noun] of a function”).
* (algebra, commutative algebra, of a ring element in a ring $B$ relative to a subring $A$) Being the root of some monic polynomial in $A$.
    Coordinate terms: integral element, algebraic
* (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

* 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
* integral kernel
* integral membrane protein
* integral number
* integral politics
* integral polygedron
* integral polynomial
* integral post-metaphysics
* integral psychology
* integral transformative practice
* integral yoga
* integrity
* semi-integral

#### Related terms

* integer
* integrity
* integrous (very rare)

#### Translations

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

### Noun

integral (plural integrals)
* (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!
** (specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.
* (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 ${\frac {1}{x}}$ on $[{\frac {1}{2}},1]$ is $\ln(2)$, but the integral of the same function on $(0,1]$ diverges. In notation, $\int _{\frac {1}{2}}^{1}{\frac {1}{x}}dx=\ln(2)$, but $\int _{0}^{1}{\frac {1}{x}}dx=\infty$.
    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: $\int _{S}\nabla \times \mathbf {F} \cdot d\mathbf {S} =\int _{\partial S}\mathbf {F} \cdot d\mathbf {r} ,$.
* (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 $x^{2}$ is ${\frac {x^{3}}{3}}$ plus a constant.
** (mathematics, historical or obsolete) The fluent of a given fluxion in Newtonian calculus.

#### Derived terms

* Barnes integral
* Choquet integral
* contour integral
* definite 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
* Volterra integral equation
* volume integral

#### Related terms

* integer

#### Translations
### Anagrams

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

## Albanian
### Noun

integral m
* (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: (Central, Balearic) [in.təˈɣɾal]
* IPA: (Valencia) [in.teˈɣɾal]

### Adjective

integral m or f (masculine and feminine plural integrals)
* integral
* (of bread, etc.) wholegrain, wholemeal

#### Related terms

* enter
* integració
* integrar
* íntegre

### Noun

integral f (plural integrals)
* (mathematics) integral

#### Derived terms

* integral indefinida

### Further reading

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

## Indonesian
### Etymology

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

### Pronunciation

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

### Adjective

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

### Noun

intêgral (plural integral-integral)
* (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)
* integral, necessary to the function of the whole
* 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: /ĩ.teˈɡɾaw/ [ĩ.teˈɡɾaʊ̯]
* (Portugal) IPA: /ĩ.tɨˈɡɾal/ [ĩ.tɨˈɣɾaɫ]
* (Portugal) IPA: /ĩ.tɨˈɡɾal/ [ĩ.tɨˈɣɾaɫ]
** (Southern Portugal) IPA: /ĩ.tɨˈɡɾa.li/ [ĩ.tɨˈɣɾa.li]
* Rhymes: -al, -aw
* Hyphenation: in‧te‧gral

### Adjective

integral m or f (plural integrais)
* integral; whole; entire
* (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)
* (mathematics) integral (limits of sums)
* (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: /in.teˈɡral/

### Adjective

integral m or n (feminine singular integrală, masculine plural integrali, feminine and neuter plural integrale)
* integral
    Synonyms: întreg, complet

#### Related terms

* integru

## Spanish
### Etymology

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

### Pronunciation

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

### Adjective

integral m or f (masculine and feminine plural integrales)
* integral
* whole
* brown (rice)
* wholegrain

#### Derived terms

* arroz integral
* cálculo integral
* integralidad
* integralmente
* pan integral
* parte integral

#### Related terms

* íntegro

### Noun

integral f (plural integrales)
* (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], 2024 December 10

## Swedish
### Etymology

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

### Pronunciation

* IPA: /ɪntɛˈɡrɑːl/
* Hyphenation: in‧te‧gral
* Rhymes: -ɑːl

### Noun

integral c
* (mathematics) an integral

#### 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: /ʔinteɡˈɾal/ [ʔɪn̪.t̪ɛɡˈɾal]
* Rhymes: -al
* Syllabification: in‧teg‧ral

### Adjective

integrál (Baybayin spelling ᜁᜈ᜔ᜆᜒᜄ᜔ᜇᜎ᜔)
* integral
    Synonyms: buo, kompleto

#### Related terms

* integrante
* integrasyon

## Turkish
### Etymology

Borrowed from French intégral.

### Pronunciation

* IPA: [in.tɛɟ.ˈɾalʲ]

### Noun

integral (definite accusative integrali, plural integraller)
* (mathematics) integral
    $\int _{a}^{b}\!f(x)\,dx\,$

#### Declension

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 :