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

Three years later, Caballero is now an integral part of the Yankees—and even Boone has changed his tune.

From The Wall Street Journal ● Jul. 23, 2026

Word of mouth and exposure - particularly through social media - have played integral roles in promoting the sport with women, organisers and competitors say.

From BBC ● Jul. 22, 2026

When you’ve had a smartphone for most of your life, it becomes an integral part of how you work, said Lindsay Boccardo, a career coach who works with Gen Z employees specifically.

From MarketWatch ● Jul. 21, 2026

Instead of Gods like Poseidon and Zeus playing an integral role in the story, they are left as unseen forces that motivate the characters’ actions.

From Salon ● Jul. 18, 2026

Fishing and hunting were an integral part of it, just as it had been part of the life of the Indians, who had practically disappeared from the Eastern Shore by 1750.

From "Harriet Tubman: Conductor on the Underground Railroad" by Ann Petry

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

Feynman integrals have plagued particle theorists since the rise of quantum field theory in the mid–20th century.

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