  # Integrity vs. Integral: What's the Difference? ## Integrity and Integral Definitions

#### Integral

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

#### Integrity

The state of being unimpaired; soundness
The building's integrity remained intact following the mild earthquake.

#### Integral

Possessing everything essential; entire.

#### Integrity

The quality or condition of being whole or undivided; completeness
Replaced a lost book to restore the integrity of his collection.

#### Integral

Expressed or expressible as or in terms of integers.

#### Integral

Expressed as or involving integrals.

#### Integrity

The state of being wholesome; unimpaired

#### Integral

A complete unit; a whole.

#### Integrity

The quality or condition of being complete; pure

#### 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.

#### Integrity

(cryptography) With regards to data encryption, ensuring that information is not altered by unauthorized persons in a way that is not detectable by authorized users.

#### Integral

A definite integral.

#### Integrity

(aviation) The ability of systems to provide timely warnings to users when they should not be used for navigation.

#### Integral

An indefinite integral.

#### Integral

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

#### Integrity

The state or quality of being entire or complete; wholeness; entireness; unbroken state; as, the integrity of an empire or territory.

#### Integral

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

#### Integrity

Moral soundness; honesty; freedom from corrupting influence or motive; - used especially with reference to the fulfillment of contracts, the discharge of agencies, trusts, and the like; uprightness; rectitude.
The moral grandeur of independent integrity is the sublimest thing in nature.
Their sober zeal, integrity, and worth.

#### Integral

(mathematics) Relating to integration.

#### Integrity

Unimpaired, unadulterated, or genuine state; entire correspondence with an original condition; purity.
Language continued long in its purity and integrity.

#### Integral

(obsolete) Whole; undamaged.

#### Integrity

An unreduced or unbroken completeness or totality

#### 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!

Moral soundness

#### 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