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

## 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.

#### Integrand➦

A function to be integrated.

#### 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

#### Integrand➦

(calculus) The function that is to be integrated

#### Integral➦

Of or denoted by an integer.

#### 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.

#### Integral➦

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

#### Integral➦

Possessing everything essential; entire.

#### Integral➦

Expressed or expressible as or in terms of integers.

#### Integral➦

Expressed as or involving integrals.

#### Integral➦

A complete unit; a whole.

#### 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.

#### Integral➦

A definite integral.

#### Integral➦

An indefinite integral.

#### Integral➦

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

#### Integral➦

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

#### Integral➦

(mathematics) Relating to integration.

#### Integral➦

(obsolete) Whole; undamaged.

#### 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!

#### Integral➦

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

#### 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 $\int_0^1\frac\left\{1\right\}\left\{x\right\} dx = \infty$.

#### 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.

#### Integral➦

The fluent of a given fluxion in Newtonian calculus.

#### Integral➦

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

#### 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.

#### Integral➦

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

#### Integral➦

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

#### Integral➦

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

#### Integral➦

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

#### 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

#### 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