integral love

# integral

## 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.

### 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, and Integration. 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 Constituting a whole together with other parts or factors; not omittable or removable
• adjective mathematics Of, pertaining to, or being an integer.
• noun mathematics 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.
• noun mathematics Antiderivative

• 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

[Middle English, from Old French, from Medieval Latin integrālis, making up a whole, from Latin integer, complete; see integer.]

From Medieval Latin integralis, from Latin integer ("entire"); see integer.

## Examples

• Of course, I disagree in that I-I "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?

• 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.

• "We had a bet about the pronunciation of the word 'integral'," he recalls.

• 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.

Archive 2009-08-01 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 self-realization 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 long-term integral average of highly varying weather) are.