# Integrity vs. Integral

## Difference Between Integrity and Integral

#### Integritynoun

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

#### Integritynoun

The state of being wholesome; unimpaired

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

#### Integritynoun

The quality or condition of being complete; pure

(mathematics) Relating to integration.

#### Integritynoun

(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.

(obsolete) Whole; undamaged.

#### Integritynoun

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

#### Integralnoun

(mathematics) A number, the limit of the sums computed in a process in which the domain of a function is divided into small subsets and a possibly nominal value of the function on each subset is multiplied by the measure of that subset, all these products then being summed.

The integral of $x\mapsto x^2$ on $\left[0,1\right]$ is $\frac\left\{1\right\}\left\{3\right\}$.

#### Integritynoun

an unreduced or unbroken completeness or totality

#### Integralnoun

(mathematics) Antiderivative

The integral of $x^2$ is $\frac\left\{x^3\right\}\left\{3\right\}$ plus a constant.

moral soundness

#### Integralnoun

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;

the Ptolemaic system with its built-in concept of periodicitya constitutional inability to tell the truth

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

a local motion keepeth bodies integralwas able to keep the collection entire during his lifetimefought to keep the union intact