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(key): /ˈɪntɪɡɹ(ə)l/ (US) enPR: ĭnʹtə-grəl, IPA(key): /ˈɪntəɡɹəl/, /ɪnˈtɛɡɹəl/ Adjective (UK) IPA(key): /ˈɪntɪɡr(ə)l/, /ɪnˈtɛɡr(ə)l/ (US) enPR: ĭn-tĕgʹrəl, IPA(key): /ˈɪntəɡɹəl/, /ɪnˈtɛɡɹəl/ === 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 (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 {\displaystyle B} relative to a subring A {\displaystyle A} ) Being the root of some monic polynomial in A {\displaystyle A} . Coordinate terms: integral element, algebraic (obsolete) Whole; undamaged. ==== Derived terms ==== ==== Related terms ==== ==== 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. (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. (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 (mathematics, historical or obsolete) The fluent of a given fluxion in Newtonian calculus. ==== Derived terms ==== ==== Related terms ==== ==== 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]‎[1], 1980 == Catalan == === Etymology === Borrowed from Medieval Latin integrālis, from Latin integer. === Pronunciation === IPA(key): (Central, Balearic) [in.təˈɣɾal] IPA(key): (Valencia) [in.teˈɣɾal] === Adjective === integral m or f (masculine and feminine plural integrals) integral (of bread, etc.) wholegrain, wholemeal ==== Related terms ==== === Noun === integral f (plural integrals) (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) 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”) Synonyms: kafi, rangkunan === Noun === intêgral (plural integral-integral) (mathematics) integral ==== Related terms ==== === Further reading === “integral”, in Kamus Besar Bahasa Indonesia [Great Dictionary of the Indonesian Language] (in Indonesian), 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 === 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 ==== === Further reading === “integral”, in Dicionário Priberam da Língua Portuguesa (in Portuguese), Lisbon: Priberam, 2008–2026 == 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/neuter plural integrale) integral Synonyms: întreg, complet ==== Declension ==== ==== Related terms ==== integru == Spanish == === Etymology === Borrowed from Medieval Latin integrālis, from Latin integer (“entire”). === Pronunciation === IPA(key): /inteˈɡɾal/ [ĩn̪.t̪eˈɣ̞ɾal] Rhymes: -al Syllabification: in‧te‧gral === Adjective === integral m or f (masculine and feminine plural integrales) integral whole brown (rice) wholegrain ==== Derived terms ==== ==== Related terms ==== === 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 23.8.1, Royal Spanish Academy [Spanish: Real Academia Española], 15 December 2025 == Swedish == === Etymology === Borrowed from Medieval Latin integrālis. === Pronunciation === IPA(key): /ɪntɛˈɡrɑːl/ Hyphenation: in‧te‧gral Rhymes: -ɑːl === Noun === integral c (mathematics) an integral ==== Declension ==== ==== 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) integral Synonyms: buo, kompleto ==== Related terms ==== == Turkish == === Etymology === Borrowed from French intégral. === Pronunciation === IPA(key): [in.tɛɟ.ˈɾalʲ] === Noun === integral (definite accusative integrali, plural integraller) (mathematics) integral ∫ a b f ( x ) d x {\displaystyle \int _{a}^{b}\!f(x)\,dx\,} ==== Declension ====