Integral vs. Nonintegral — What's the Difference?

Necessary to make a whole complete.

Apart from the essential nature of something.

Being an essential part of something.

Not necessary or essential for completeness.

Necessary for completeness.

Not central or fundamental.

Constituting the entirety of something.

Not constituting a necessary element of a whole.

Fundamental or central to the nature of something.

Can be excluded without affecting the whole significantly.

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.

(mathematics) Not integral.

Necessary to make a whole complete; essential or fundamental

Of or denoted by an integer.

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.

Essential or necessary for completeness; constituent

Possessing everything essential; entire.

Expressed or expressible as or in terms of integers.

Expressed as or involving integrals.

A complete unit; a whole.

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.

A definite integral.

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.

(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.

(specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.

(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.

(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 fluent of a given fluxion in Newtonian calculus.

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

Essential to completeness; constituent, as a part; pertaining to, or serving to form, an integer; integrant.

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

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

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

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;

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

It helps in prioritizing components for development, maintenance, and resource allocation, ensuring that essential parts are given precedence.

A component is integral if it is essential to the function, operation, or identity of a whole, such that its absence would significantly alter or impair the whole.

A role might have aspects that are integral and others that are nonintegral, but roles themselves are generally categorized based on their core responsibilities.

Yes, through changes in design, function, or user needs, a nonintegral part can become integral.

While it may affect performance or convenience, it does not compromise the system's basic functionality or purpose.

Yes, the context or framework in which something is considered can determine whether it is seen as integral or nonintegral.

Generally, yes, unless the aesthetic element is central to the identity or functionality of the item, as might be the case in design-centric products.

It refers to integration, a core concept in calculus essential for calculating areas under curves and solving differential equations.

Integral parts are crucial for functionality or completeness, while nonintegral parts are less important and can be removed without significant impact.

Not necessarily. Integral parts are defined by their necessity, not their cost or complexity.

In teams, integral roles are critical to achieving objectives, while nonintegral roles may support team cohesion or provide supplementary skills.

Integral elements are prioritized in the design process to ensure the system or product meets its essential functions and objectives.

Yes, as technologies evolve and user needs change, the significance of parts can shift between integral and nonintegral.

While guidelines exist, the distinction can sometimes be subjective and dependent on specific circumstances or perspectives.

It helps in setting priorities, allocating resources effectively, and managing risks by focusing on essential components.