# Integral vs. Integer — What's the Difference?

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## Compare with Definitions

#### Integral

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.
Sep 20, 2019

#### Integer

An integer (from the Latin integer meaning "whole") is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.
Sep 20, 2019

#### Integral

Of or denoted by an integer.
Sep 20, 2019

#### Integer

A member of the set of positive whole numbers {1, 2, 3, ... }, negative whole numbers {-1, -2, -3, ... }, and zero {0}.
Sep 20, 2019

#### Integral

Necessary to make a whole complete; essential or fundamental
Games are an integral part of the school's curriculum
Systematic training should be integral to library management
Sep 20, 2019
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#### Integer

A number which is not a fraction; a whole number
Integer values
Sep 20, 2019

#### Integral

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.
Sep 20, 2019

#### Integer

A thing complete in itself.
Sep 20, 2019

#### Integral

Essential or necessary for completeness; constituent
The kitchen is an integral part of a house.
Sep 20, 2019

#### Integer

A complete unit or entity.
Sep 20, 2019

#### Integral

Possessing everything essential; entire.
Sep 20, 2019

#### Integer

(arithmetic) A number that is not a fraction; an element of the infinite and numerable set {..., -3, -2, -1, 0, 1, 2, 3, ...}.
Sep 20, 2019

#### Integral

Expressed or expressible as or in terms of integers.
Sep 20, 2019

#### Integer

A complete entity; a whole number, in contradistinction to a fraction or a mixed number.
Sep 20, 2019

#### Integral

Expressed as or involving integrals.
Sep 20, 2019

#### Integer

Any of the natural numbers (positive or negative) or zero
Sep 20, 2019

#### Integral

A complete unit; a whole.
Sep 20, 2019

#### Integral

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.
Sep 20, 2019

#### Integral

A definite integral.
Sep 20, 2019

#### Integral

An indefinite integral.
Sep 20, 2019

#### Integral

Constituting a whole together with other parts or factors; not omittable or removable
Sep 20, 2019

#### Integral

(mathematics) Of, pertaining to, or being an integer.
Sep 20, 2019

#### Integral

(mathematics) Relating to integration.
Sep 20, 2019

#### Integral

(obsolete) Whole; undamaged.
Sep 20, 2019

#### Integral

(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.
The integral of a univariate real-valued function is the area under its curve; but be warned! Not all functions are integrable!
Sep 20, 2019

#### Integral

(specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.
Sep 20, 2019

#### Integral

(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.
The integral of $\frac\left\{1\right\}\left\{x\right\}$ on $\left[\frac\left\{1\right\}\left\{2\right\}, 1\right]$ is $\ln\left(2\right)$, but the integral of the same function on $\left(0, 1\right]$ diverges. In notation, $\int_\frac\left\{1\right\}\left\{2\right\}^1\frac\left\{1\right\}\left\{x\right\} dx = \ln\left(2\right)$, but $\int_0^1\frac\left\{1\right\}\left\{x\right\} dx = \infty$.
Sep 20, 2019

#### Integral

(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;
The integral of $x^2$ is $\frac\left\{x^3\right\}\left\{3\right\}$ plus a constant.
Sep 20, 2019

#### Integral

The fluent of a given fluxion in Newtonian calculus.
Sep 20, 2019

#### Integral

Lacking nothing of completeness; complete; perfect; uninjured; whole; entire.
A local motion keepeth bodies integral.
Sep 20, 2019

#### Integral

Essential to completeness; constituent, as a part; pertaining to, or serving to form, an integer; integrant.
Ceasing to do evil, and doing good, are the two great integral parts that complete this duty.
Sep 20, 2019

#### Integral

Of, pertaining to, or being, a whole number or undivided quantity; not fractional.
Sep 20, 2019

#### Integral

A whole; an entire thing; a whole number; an individual.
Sep 20, 2019

#### Integral

An expression which, being differentiated, will produce a given differential. See differential Differential, and Integration. Cf. Fluent.
Sep 20, 2019

#### Integral

The result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)
Sep 20, 2019

#### Integral

Existing as an essential constituent or characteristic;
The Ptolemaic system with its built-in concept of periodicity
A constitutional inability to tell the truth
Sep 20, 2019

#### Integral

Constituting the undiminished entirety; lacking nothing essential especially not damaged;
A local motion keepeth bodies integral
Was able to keep the collection entire during his lifetime
Fought to keep the union intact
Sep 20, 2019

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