Definitions
from The American Heritage® Dictionary of the English Language, 5th Edition.
 adjective Essential or necessary for completeness; constituent.
 adjective Possessing everything essential; entire.
 adjective Expressed or expressible as or in terms of integers.
 adjective Expressed as or involving integrals.
 noun A complete unit; a whole.
 noun 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.
 noun A definite integral.
 noun An indefinite integral.
from The Century Dictionary.
 Total.
 Relating to a whole composed of parts spatially distinct (as a human body of head, trunk, and limbs), or of distinct units (as a number).
 Hence, and by a reversion to the classical meaning of integer
 Unmaimed; unimpaired.
 Intrinsic; belonging as a part to the whole, and not a mere appendage to it.
 In mathematics: Of, pertaining to, or being a whole number or undivided quantity.
 Pertaining to or proceeding by integration: as, the integral method.
 noun An integral whole; a whole formed of parts spatially distinct, or of numerical parts.
 noun An integral part.
 noun In mathematics, the result of integration, or the operation inverse to differentiation.
 noun See the adjectives.
from the GNU version of the Collaborative International Dictionary of English.
 noun A whole; an entire thing; a whole number; an individual.
 noun (Math.) An expression which, being differentiated, will produce a given differential. See differential
Differential , andIntegration . Cf.Fluent .  noun one of an important class of integrals, occurring in the higher mathematics;  so called because one of the integrals expresses the length of an arc of an
ellipse .  adjective Lacking nothing of completeness; complete; perfect; uninjured; whole; entire.
 adjective Essential to completeness; constituent, as a part; pertaining to, or serving to form, an integer; integrant.
 adjective Of, pertaining to, or being, a whole number or undivided quantity; not fractional.
 adjective Pertaining to, or proceeding by, integration.
 adjective See under
Calculus .
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 adjective
Constituting awhole together with otherparts orfactors ; notomittable orremovable  adjective mathematics Of, pertaining to, or being an
integer .  noun mathematics A number, the
limit of the sums computed in a process in which thedomain of afunction is divided into smallsubsets and a possibly nominal value of the function on each subset is multiplied by themeasure of that subset, all these products then being summed.  noun mathematics
Antiderivative
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 noun the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)
 adjective constituting the undiminished entirety; lacking nothing essential especially not damaged
 adjective existing as an essential constituent or characteristic
 adjective of or denoted by an integer
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/ShareAlike License
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Examples

Of course, I disagree in that II "owns", in any meaningful sense, the term integral, or that "they ARE the authority".
Integral and Copyright Tusar N Mohapatra 2006

Is the term integral or superfluous to the substance of these papers?
Must read: National Academy of Sciences member says Darwinism "contributes little" to experimental biology Denyse O 2005

Is the term integral or superfluous to the substance of these papers?
Response to NAS member's critique of the usefulness of Darwinism: Denyse O 2005

"We had a bet about the pronunciation of the word 'integral'," he recalls.
Telegraph.co.uk  Telegraph online, Daily Telegraph and Sunday Telegraph 2011

"We had a bet about the pronunciation of the word 'integral'," he recalls.
Telegraph.co.uk  Telegraph online, Daily Telegraph and Sunday Telegraph 2011

The Lebesgue integral is at the heart of measure theory and probability theory, and I had long thought of it as elegant but difficult to visualize.

In your reading, how integral is social critique to the novel?
The Elegance of the Hedgehog by Muriel Barbery: Questions 2008

The word integral means for this paradigm recognizing the value of all of the stages... each emergence is absorbed in the next.
Archive 20090801 Tusar N Mohapatra 2009

The word integral means for this paradigm recognizing the value of all of the stages... each emergence is absorbed in the next.
Ontology as selfrealization Tusar N Mohapatra 2009

Basic assumption of natural science is that things happen for a reason (aside from natural oscillation around equilibrium point), and in climate science what scientists are trying to figure out is what exactly these reasons for climate change (climate as being of longterm integral average of highly varying weather) are.
sam commented on the word integral
An integral is the result of integration. The intergrand is the expression that you integrate.
December 9, 2006