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

## Compare with Definitions

#### Intricate

Having many complexly arranged elements; elaborate
An intricate pattern.
An intricate procedure.

#### 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.

#### Intricate

Difficult to understand, analyze, or solve for having many interconnected elements.

#### 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

#### Intricate

Having a great deal of fine detail or complexity.
The architecture of this clock is very intricate.

#### Integral

Of or denoted by an integer.

#### Intricate

(intransitive) To become enmeshed or entangled.

#### 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.

#### Intricate

(transitive) To enmesh or entangle: to cause to intricate.

#### Integral

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

#### Intricate

Entangled; involved; perplexed; complicated; difficult to understand, follow, arrange, or adjust; as, intricate machinery, labyrinths, accounts, plots, etc.
His style was fit to convey the most intricate business to the understanding with the utmost clearness.
The nature of man is intricate.

#### Integral

Possessing everything essential; entire.

#### Intricate

To entangle; to involve; to make perplexing.
It makes men troublesome, and intricates all wise discourses.

#### Integral

Expressed or expressible as or in terms of integers.

#### Intricate

Highly involved or intricate;
The Byzantine tax structure
Convoluted legal language
Convoluted reasoning
Intricate needlework
An intricate labyrinth of refined phraseology
The plot was too involved
A knotty problem
Got his way by labyrinthine maneuvering
Oh, what a tangled web we weave
Tortuous legal procedures
Tortuous negotiations lasting for months

#### 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