# Integral vs. Integrand

## Difference Between Integral and Integrand

Essential or necessary for completeness; constituent

The kitchen is an integral part of a house.

#### Integrandnoun

A function to be integrated.

Possessing everything essential; entire.

#### Integrandnoun

(calculus) The function that is to be integrated

Expressed or expressible as or in terms of integers.

Expressed as or involving integrals.

#### Integralnoun

A complete unit; a whole.

#### Integralnoun

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.

#### Integralnoun

A definite integral.

#### Integralnoun

An indefinite integral.

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

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

(mathematics) Relating to integration.

(obsolete) Whole; undamaged.

#### 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 $\frac\left\{1\right\}\left\{3\right\}$.

#### Integralnoun

(mathematics) Antiderivative

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

#### 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