Integral vs. Integer — What's the Difference?
Difference Between Integral and Integer
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Definitions
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.
Integer
An integer (from the Latin integer meaning "whole") is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.
Integral
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
Integer
A member of the set of positive whole numbers {1, 2, 3, ... }, negative whole numbers {-1, -2, -3, ... }, and zero {0}.
Integral
Of or denoted by an integer.
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Integer
A number which is not a fraction; a whole number
Integer values
Integral
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.
Integer
A thing complete in itself.
Integral
Essential or necessary for completeness; constituent
The kitchen is an integral part of a house.
Integer
A complete unit or entity.
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Integral
Possessing everything essential; entire.
Integer
(arithmetic) A number that is not a fraction; an element of the infinite and numerable set {..., -3, -2, -1, 0, 1, 2, 3, ...}.
Integral
Expressed or expressible as or in terms of integers.
Integer
A complete entity; a whole number, in contradistinction to a fraction or a mixed number.
Integral
Expressed as or involving integrals.
Integer
Any of the natural numbers (positive or negative) or zero
Integral
A complete unit; a whole.
Integral
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.
Integral
A definite integral.
Integral
An indefinite integral.
Integral
Constituting a whole together with other parts or factors; not omittable or removable
Integral
(mathematics) Of, pertaining to, or being an integer.
Integral
(mathematics) Relating to integration.
Integral
(obsolete) Whole; undamaged.
Integral
(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.
The integral of a univariate real-valued function is the area under its curve; but be warned! Not all functions are integrable!
Integral
(specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.
Integral
(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.
The integral of on is , but the integral of the same function on diverges. In notation, , but .
Integral
(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 integral of is plus a constant.
Integral
The fluent of a given fluxion in Newtonian calculus.
Integral
Lacking nothing of completeness; complete; perfect; uninjured; whole; entire.
A local motion keepeth bodies integral.
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.
Integral
Of, pertaining to, or being, a whole number or undivided quantity; not fractional.
Integral
A whole; an entire thing; a whole number; an individual.
Integral
An expression which, being differentiated, will produce a given differential. See differential Differential, and Integration. Cf. Fluent.
Integral
The result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)
Integral
Existing as an essential constituent or characteristic;
The Ptolemaic system with its built-in concept of periodicity
A constitutional inability to tell the truth
Integral
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