English Explanatory Dictionary

integral

English dictionary entry

Meanings

adj
  1. Constituting a whole together with other parts or factors; not omittable or removable.
  2. Of, pertaining to, or being an integer.
  3. Relating to integration (“the process of finding the integral [noun] of a function”).
  4. Being the root of some monic polynomial in A.
  5. Whole; undamaged.
noun
  1. 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.
  2. Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.
  3. 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.
  4. 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;
  5. The fluent of a given fluxion in Newtonian calculus.
name
  1. Abbreviation of International Gamma-Ray Astrophysics Laboratory (a satellite of the European Space Agency).

Pronunciation

/ˈɪntɪɡr(ə)l/ /ɪnˈtɛɡr(ə)l/ ĭn-tĕgʹrəl /ˈɪntəɡɹəl/ /ɪnˈtɛɡɹəl/ en-uk-integral-adjective.ogg ĭnʹtĭ-grəl /ˈɪntɪɡɹ(ə)l/ ĭnʹtə-grəl en-uk-integral-noun.ogg

Word forms

integral more integral most integral integrals

Etymology

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

Synonyms

immanent inherent necessary built-in essential inborn resident inbuilt infused ingrained integral intrinsic inwrought radical antiderivative indefinite integral mul:∫

Antonyms

derivative

Related words

integer integrity integrous integrate

Derived words

differintegral 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 integralism integralist integrality integral kernel integrally integral membrane protein integralness integral number integral politics integral polygedron integral polynomial integral post-metaphysics integral psychology integral transformative practice integral yoga integraph integrity nonintegral semi-integral unintegral Barnes integral Choquet integral contour integral definite integral double integral flux 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

Translations

Arabic: تَكَامُل Armenian: ինտեգրալ Belarusian: інтэгра́л Bulgarian: интегра́л Catalan: integració Chinese Cantonese: 積分 /积分 Hakka Chinese: chit-fûn-ho̍k Chinese Mandarin: 積分 /积分 Czech: integrál Dutch: integraal Esperanto: integralo Esperanto: integro Finnish: integraali French: intégrale Galician: integral Georgian: ინტეგრალი German: Integral Greek: ολοκλήρωμα Hebrew: אִינְטֶגְרָל Hebrew: אַסְכֶּמֶת Hungarian: integrál Icelandic: heildun Icelandic: tegrun Italian: integrale Japanese: 積分 Kazakh: интеграл Khmer: អាំងតេក្រាល Korean: 적분 Kyrgyz: интеграл Malay: kamiran Manx: co-hym Mongolian: интеграл Norwegian: integral Polish: całka Polish: całka oznaczona Portuguese: integral Romanian: integrală Russian: интегра́л Serbo-Croatian: интѐгра̄л Serbo-Croatian: intègrāl Spanish: integral Sundanese: integral Swedish: integral Tagalog: lagom Thai: ปริพันธ์
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