Integrated vs. Integral — What's the Difference?

To make into a whole by bringing all parts together; unify

In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration.

To join with something else; unite

Necessary to make a whole complete; essential or fundamental

To make part of a larger unit

Of or denoted by an integer.

To open (an institution, for example) to people of all races or ethnic groups without restriction; desegregate.

A function of which a given function is the derivative, i.e. which yields that function when differentiated, and which may express the area under the curve of a graph of the function.

To admit (a racial or ethnic group) to equal membership in an institution or society.

Essential or necessary for completeness; constituent

To calculate the integral of.

Possessing everything essential; entire.

To perform integration on.

Expressed or expressible as or in terms of integers.

(Psychology) To bring about the integration of (personality traits).

Expressed as or involving integrals.

To become integrated or undergo integration.

A complete unit; a whole.

Composed and coordinated to form a whole

A number computed by a limiting process in which the domain of a function, often an interval or planar region, is divided into arbitrarily small units, the value of the function at a point in each unit is multiplied by the linear or areal measurement of that unit, and all such products are summed.

(US) characterized by racial integration

A definite integral.

Simple past tense and past participle of integrate

An indefinite integral.

Formed or united into a whole.

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

Formed into a whole or introduced into another entity; as, an integrated Europe. Opposite of nonintegrated.

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

Having different groups treated together as equals in one group; as, racially integrated schools.

(mathematics) Relating to integration.

Resembling a living organism in organization or development.

(obsolete) Whole; undamaged.

Combined. Opposite of uncombined.

(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.

Having constituent parts mixed to form a single unit. Opposite of unmixed.

(specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.

Formed or united into a whole

(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.

Formed into a whole or introduced into another entity;

(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;

Not segregated; designated as available to all races or groups;

The fluent of a given fluxion in Newtonian calculus.

Resembling a living organism in organization or development;

Lacking nothing of completeness; complete; perfect; uninjured; whole; entire.

Caused to combine or unite

Essential to completeness; constituent, as a part; pertaining to, or serving to form, an integer; integrant.

Of, pertaining to, or being, a whole number or undivided quantity; not fractional.

A whole; an entire thing; a whole number; an individual.

An expression which, being differentiated, will produce a given differential. See differential Differential, and Integration. Cf. Fluent.

The result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)

Existing as an essential constituent or characteristic;

Constituting the undiminished entirety; lacking nothing essential especially not damaged;