integral

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.

   The integral of a univariate real-valued function is the area under its curve; but be warned! Not all functions are integrable!

   Integral

   интегра́лintɛgrál

   інтегра́лintehrál

2. 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.

   (конкретно)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;

   The integral of x² is #92;frac#123;x³#125;#123;3#125; plus a constant.

5. 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;

   (історичне, застаріле)The fluent of a given fluxion in Newtonian calculus.

1. Death is an integral part of life.

   Смерть - це невід'ємна частина життя.

   ruСмерть - это неотъемлемая часть жизни.

   deDer Tod ist ein fester Bestandteil des Lebens.

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2. Fluence is the time integral of flux.

   ruФлюенс - это интеграл по времени от потока.

   deDie Fluenz ist das Zeitintegral des Flusses.

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3. Improvisation is an integral part of jazz.

   ruИмпровизация - неотъемлемая часть джаза.

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4. The meaning is an integral part of the word.

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5. An antiderivative and an integral aren't exactly the same.

   deStammfunktion und Integral sind nicht genau das Gleiche.

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