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

Explanation

Something that is integral is very important or necessary. If you are an integral part of the team, it means that the team cannot function without you. An integral part is necessary to complete the whole. In this sense, the word essential is a near synonym. In mathematics, there are integrals of functions and equations. Integral is from Middle English, from Medieval Latin integralis "making up a whole," from Latin integer "untouched, entire."

Example Sentences

Collins held leadership roles at HBO, Time Warner Cable and Comcast, and was integral to the Telecommunications Act of 1996.

From The Wall Street Journal • Apr. 16, 2026

Identifying and helping cultivate fresh storylines driven by relatable characters are integral to that success.

From Los Angeles Times • Apr. 13, 2026

The crew themselves have been integral to the storytelling.

From Barron's • Apr. 11, 2026

After that mess, Mr. Rousseau promised to learn to speak French, and the chairman of the Air Canada board vowed that it would be “an integral part” of his performance evaluation.

From The Wall Street Journal • Apr. 7, 2026

She answered the phones and distributed the mail in addition to her regular duties, which at the time involved solving a triple integral for an engineer in the division.

From "Hidden Figures" by Margot Lee Shetterly

Related Words

• elemental
• essential
• indispensable
• intrinsic