integral
English edit
Etymology edit
Borrowed from Middle French integral, from Medieval Latin integrālis, from Latin integer (“entire”); see integer.
Pronunciation edit
- 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 edit
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, 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.
- (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 relative to a subring ) Being the root of some monic polynomial in .
- Coordinate terms: integral element, algebraic
- (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.
Derived terms edit
- 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 politics
- integral polygedron
- integral polynomial
- integral post-metaphysics
- integral psychology
- integral transformative practice
- integral yoga
- integrity
- semi-integral
Related terms edit
Translations edit
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- The translations below need to be checked and inserted above into the appropriate translation tables. See instructions at Wiktionary:Entry layout § Translations.
Noun edit
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 on is , but the integral of the same function on diverges. In notation, , but .
- 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: .
- (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 is plus a constant.
- Synonyms: antiderivative, indefinite integral, ∫
- Antonym: derivative
- (mathematics, historical or obsolete) The fluent of a given fluxion in Newtonian calculus.
Derived terms edit
- 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 edit
Translations edit
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Anagrams edit
Albanian edit
Noun edit
integral m
- (mathematics) integral (relating to integration)
Further reading edit
Catalan edit
Etymology edit
Borrowed from Medieval Latin integrālis, from Latin integer.
Pronunciation edit
Adjective edit
integral m or f (masculine and feminine plural integrals)
- integral
- (of bread, etc.) wholegrain, wholemeal
Related terms edit
Noun edit
integral f (plural integrals)
Derived terms edit
Further reading edit
- “integral” in Diccionari de la llengua catalana, segona edició, Institut d’Estudis Catalans.
Middle French edit
Etymology edit
Borrowed from Medieval Latin integrālis, from Latin integer.
Adjective edit
integral m (feminine singular integrale, masculine plural integraux, feminine plural integrales)
Descendants edit
- French: intégral
References edit
- integral on Dictionnaire du Moyen Français (1330–1500) (in French)
Portuguese edit
Etymology edit
Borrowed from Medieval Latin integrālis, from Latin integer (“entire; untouched”).
Pronunciation edit
Adjective edit
integral m or f (plural integrais)
Quotations edit
For quotations using this term, see Citations:integral.
Synonyms edit
Derived terms edit
Noun edit
integral f or m (plural integrais)
- (mathematics) integral (limits of sums)
- (mathematics) antiderivative
- Synonym: antiderivada
Quotations edit
For quotations using this term, see Citations:integral.
Related terms edit
Further reading edit
Romanian edit
Etymology edit
Borrowed from French intégral, Medieval Latin integrālis.
Pronunciation edit
Adjective edit
integral m or n (feminine singular integrală, masculine plural integrali, feminine and neuter plural integrale)
Declension edit
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 | integralelor | integralilor |
Related terms edit
Spanish edit
Etymology edit
Borrowed from Medieval Latin integrālis, from Latin integer (“entire”).
Pronunciation edit
- IPA(key): /inteˈɡɾal/ [ĩn̪.t̪eˈɣ̞ɾal]
Audio (Colombia): (file) - Rhymes: -al
- Syllabification: in‧te‧gral
Adjective edit
integral m or f (masculine and feminine plural integrales)
- integral
- whole
- brown (rice)
- wholegrain
Derived terms edit
Related terms edit
Noun edit
integral f (plural integrales)
Further reading edit
- “integral”, in Diccionario de la lengua española, Vigésima tercera edición, Real Academia Española, 2014
Swedish edit
Etymology edit
(This etymology is missing or incomplete. Please add to it, or discuss it at the Etymology scriptorium.)
Pronunciation edit
Noun edit
integral c
- (mathematics) an integral
Declension edit
Declension of integral | ||||
---|---|---|---|---|
Singular | Plural | |||
Indefinite | Definite | Indefinite | Definite | |
Nominative | integral | integralen | integraler | integralerna |
Genitive | integrals | integralens | integralers | integralernas |
Related terms edit
References edit
- integral in Svensk ordbok (SO)
- integral in Svenska Akademiens ordlista (SAOL)
- integral in Svenska Akademiens ordbok (SAOB)
Anagrams edit
Tagalog edit
Etymology edit
Borrowed from Spanish integral.
Pronunciation edit
Adjective edit
integrál (Baybayin spelling ᜁᜈ᜔ᜆᜒᜄ᜔ᜇᜎ᜔)
Related terms edit
Turkish edit
Etymology edit
Borrowed from French intégral.
Pronunciation edit
Noun edit
integral (definite accusative integrali, plural integraller)