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

But he adds that mariachi, ubiquitous in Mexico and L.A., is also an integral part of Venezuelan culture.

From Los Angeles Times • May 19, 2026

The stories frame the all-consuming desire for retaliation as an integral aspect of our mortal lives; no one gets out without hankering for a bit of vengeance.

From Salon • May 19, 2026

Neither fully captures how this has become an integral and increasingly difficult to replace relationship between two neighbouring countries who, despite their asymmetries and differences, share vital interests.

From BBC • May 18, 2026

Crow noted that she chose Nashville because she already had family living in the area, family that would become an integral part of her decision to adopt two children as a single mother.

From MarketWatch • May 18, 2026

The Pythagorean idea of a perfect and mystical world, unseen by the senses, was readily accepted by the early Christians and was an integral component of Kepler’s early training.

From "Cosmos" by Carl Sagan

Related Words

• elemental
• essential
• indispensable
• intrinsic