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

• integrals
  plural

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

Derived Forms

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

Inflected Forms

Nouns

• integrals
  plural

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

See Examples For:

integral integrals

DR20 now includes integral field spectroscopy maps of 6 separate target regions covering 169 tiles and about 300,000 spectra.

From Science Daily ● Aug. 14, 2026

Rather than relying on elaborate studio sets, the production embraced the neighborhood’s authentic character, allowing real businesses, public squares, and residential streets to become integral parts of the series’ identity.

From MarketWatch ● Aug. 10, 2026

The authors conclude that wildfire prevention should be an integral part of protected-area management.

From The Wall Street Journal ● Aug. 9, 2026

“I have come to love talking about it in the context of women’s empowerment, finding ways to embrace their own integral agency.”

From Los Angeles Times ● Aug. 6, 2026

Times photographers, coordinated by a superb picture editor, Sarah Weissman, were partners from the outset in most of the reporting, and produced portraits integral to the project.

From "Class Matters" by The New York Times

Calculations involving proton vibrational wavefunction overlap integrals supported this interpretation.

From Science Daily ● Jul. 22, 2026

These integrals help determine which excited-state relaxation pathways are favored and steer the system toward efficient triplet energy migration.

From Science Daily ● Jul. 22, 2026

For decades, researchers have depended on indirect computational techniques such as molecular dynamics and Monte Carlo simulations to estimate configurational integrals.

From Science Daily ● Mar. 15, 2026

That produces a set of differential equations relating all of the master integrals.

From Science Magazine ● Nov. 30, 2022

“Yeah! Susie herself. That robot’s a mathematical wiz. He knows all about everything plus a bit on the side. He does triple integrals in his head and eats up tensor analysis for dessert.”

From "I, Robot" by Isaac Asimov

Related Words

• elemental
• essential
• indispensable
• intrinsic