integral

American  

[in-ti-gruhl, in-teg-ruhl] / ˈɪn tɪ grəl, ɪnˈtɛg rəl /

adjective

1. of, relating to, or belonging as a part of the whole; constituent or component.

   integral parts.

2. necessary to the completeness of the whole.

   This point is integral to his plan.

   Synonyms:

   requisite, indispensable, essential

3. consisting or composed of parts that together constitute a whole.

4. entire; complete; whole.

   the integral works of a writer.

5. Arithmetic. pertaining to or being an integer; not fractional.

6. Mathematics. pertaining to or involving integrals.

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noun

1. an integral whole.

2. Mathematics.

   1. Also called Riemann integral.  the numerical measure of the area bounded above by the graph of a given function, below by the x -axis, and on the sides by ordinates drawn at the endpoints of a specified interval; the limit, as the norm of partitions of the given interval approaches zero, of the sum of the products of the function evaluated at a point in each subinterval times the length of the subinterval.

   2. a primitive.

   3. any of several analogous quantities.

integral British  

/ ˌɪntɪˈɡrælɪtɪ /

adjective

1. (often foll by to) being an essential part (of); intrinsic (to)

2. intact; entire

3. formed of constituent parts; united

4. maths

   1. of or involving an integral

   2. involving or being an integer

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noun

1.  ʃ.  maths the limit of an increasingly large number of increasingly smaller quantities, related to the function that is being integrated (the integrand). The independent variables may be confined within certain limits ( definite integral ) or in the absence of limits ( indefinite integral )

2. a complete thing; whole

integral Scientific  

/ ĭn′tĭ-grəl /

1. Involving or expressed as an integer or integers.

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1. See definite integral indefinite integral

Other Word Forms

• integrality noun
• integrally adverb
• unintegral adjective
• unintegrally adverb

Etymology

Origin of integral

From the Medieval Latin word integrālis, dating back to 1545–55. See integer, -al ¹

Example Sentences

These designs stand out visually, but they also make it possible to write explicit integral representations of functions, which are essential for solving complex boundary value problems.

From Science Daily

“There’s only one park in the world that has that fountain, that’s such an integral part of history.”

From The Wall Street Journal

Franklin, who died in 1958, is today recognised for the integral role she played in the scientific breakthrough of DNA research, despite her work largely being written out of the story at the time.

From BBC

However, the region has remained largely unrecognised on the global stage and Somalia considers Somaliland to be an integral part of its territory.

From BBC

China says its right to the area goes back centuries to when these island chains were regarded as integral parts of the Chinese nation.

From BBC

Related Words

• elemental
• essential
• indispensable
• intrinsic