Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 adj. Essential or necessary for completeness; constituent: The kitchen is an integral part of a house.
 adj. Possessing everything essential; entire.
 adj. Mathematics Expressed or expressible as or in terms of integers.
 adj. Mathematics Expressed as or involving integrals.
 n. A complete unit; a whole.
 n. Mathematics 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.
 n. Mathematics A definite integral.
 n. Mathematics An indefinite integral.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Constituting a whole together with other parts or factors; not omittable or removable
 adj. Of, pertaining to, or being an integer.
 n. 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.
 n. Antiderivative
from the GNU version of the Collaborative International Dictionary of English
 adj. Lacking nothing of completeness; complete; perfect; uninjured; whole; entire.
 adj. Essential to completeness; constituent, as a part; pertaining to, or serving to form, an integer; integrant.
 adj.
 adj. Of, pertaining to, or being, a whole number or undivided quantity; not fractional.
 adj. Pertaining to, or proceeding by, integration.
 n. A whole; an entire thing; a whole number; an individual.
 n. An expression which, being differentiated, will produce a given differential. See differential Differential, and Integration. Cf. Fluent.
from The Century Dictionary and Cyclopedia
 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.
 n. An integral whole; a whole formed of parts spatially distinct, or of numerical parts.
 n. An integral part.
 n. In mathematics, the result of integration, or the operation inverse to differentiation.
 n. See the adjectives.
 Total.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)
 adj. constituting the undiminished entirety; lacking nothing essential especially not damaged
 adj. existing as an essential constituent or characteristic
 adj. of or denoted by an integer
Etymologies
Examples

Of course, I disagree in that II "owns", in any meaningful sense, the term integral, or that "they ARE the authority".

Is the term integral or superfluous to the substance of these papers?

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

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 word integral means for this paradigm recognizing the value of all of the stages... each emergence is absorbed in the next.

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.

For me the significance of the word integral springs from its mathematical sense: relating to a whole, wholeness; and rests in the recognition that we err when we regard the one as made up of the many  unity in multiplicity  but that we have the truth when we know that the Many are the One in Manifestation  Multiplicity in Unity.

In its most radical forms, such as analytical cubism or the writings of Gertrude Stein, it calls the integral subject into doubt by multiplying edges and frames and beginnings and repetitions till one cannot see the object represented as having an interior or center.

This question remains a live one; my intention here is only to frame it for further inquiry in order to show that what we call integral critique at the time of capital’s explicitly imperial period responded directly in form and content to the conditions of an imperial regime.
Like Hegel, Sri Aurobindo characterizes this evolution as Providential
sam commented on the word integral
An integral is the result of integration. The intergrand is the expression that you integrate.
December 9, 2006