Integral vs. Important — What's the Difference?

Constituting an essential part.

Having serious meaning or worth.

Cannot be omitted without impairing the whole.

Deserving of attention; likely to have a profound effect.

Necessary to form a complete whole.

Of great significance or value.

Essential for completeness or wholeness.

Weighty or consequential.

Being a necessary part of something.

Key to a particular process or outcome.

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.

Strongly affecting the course of events or the nature of things; significant

Necessary to make a whole complete; essential or fundamental

Having high social rank or influence; prominent

Of or denoted by an integer.

Having or suggesting a consciousness of high position or authority; authoritative

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.

(Obsolete) Importunate.

Essential or necessary for completeness; constituent

Having relevant and crucial value.

Possessing everything essential; entire.

(obsolete) Pompous; self-important.

Expressed or expressible as or in terms of integers.

Full of, or burdened by, import; charged with great interests; restless; anxious.

Expressed as or involving integrals.

Carrying or possessing weight or consequence; of valuable content or bearing; significant; weighty.

A complete unit; a whole.

Bearing on; forcible; driving.

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.

Importunate; pressing; urgent.

A definite integral.

Of great significance or value;

An indefinite integral.

Important in effect or meaning;

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

Of extreme importance; vital to the resolution of a crisis;

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

Having authority or ascendancy or influence;

(mathematics) Relating to integration.

Having or suggesting a consciousness of high position;

(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;

Yes, integral specifically refers to essential parts that make a whole, whereas important has a broader implication of value and influence.

If it's essential for completeness and cannot be removed without changing the fundamental nature, it's integral.

Assess if removing it would alter the essential structure or function of the whole.

It helps in prioritizing components and understanding their roles within a system.

Recognizing the importance of an element helps in allocating resources, attention, and effort effectively to maximize impact.

Yes, if it carries significant value or influence but isn't necessary for the structure’s completeness.

A CEO is integral to a company's leadership and direction, as their role is central to decision-making and strategy implementation.

In a mechanical system, integral parts are those necessary for operation, like gears in a watch; in a team, integral members contribute skills essential for the team’s success.

Yes, as systems or relationships evolve, elements that were once merely important can become essential to their functioning.

Yes, in crisis situations, important elements such as emergency response plans may overshadow integral daily operations, focusing on immediate needs and impacts.