VS.

# Integral vs. Integrand

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

Integrandnoun

(calculus) The function that is to be integrated

(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.’;

Lacking nothing of completeness; complete; perfect; uninjured; whole; entire.

‘A local motion keepeth bodies 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.’;

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

Integralnoun

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

Integralnoun

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

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 periodicity’; ‘a constitutional inability to tell the truth’;

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’;

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’;

included as part of a whole rather than supplied separately

‘the unit comes complete with integral pump and heater’;

having all the parts that are necessary to be complete

‘the first integral recording of the ten Mahler symphonies’;

of or denoted by an integer.

involving only integers, especially as coefficients of a function.

Integralnoun

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.

Integralnoun

a function satisfying a given differential equation.

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.