integral

noun

(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;

(space science, ESA) Abbreviation of International Gamma-Ray Astrophysics Laboratory (a satellite of the European Space Agency).

(mathematics, historical or obsolete) The fluent of a given fluxion in Newtonian calculus.

adjective

Constituting a whole together with other parts or factors; not omittable or removable.

(mathematics) Relating to integration (“the process of finding the integral [noun] of a function”).

(mathematics) Of, pertaining to, or being an integer.

(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.

(obsolete) Whole; undamaged.

Roots

tangotegr- · Latin · touch

Synonyms for integral

integrantadj entireadj integratedadj essentialadj intactadj componentn irreducibleadj intrinsicadj fundamentaladj indivisibleadj

Synonyms & related words for integral

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Words related to integral

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Synonyms for integral

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Where does integral come from?

The word integral breaks down into one root of Latin origin: the root tegr-, from Latin tango (“touch”). Explore each root to see other English words built from the same source.