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.

---

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

---

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.

---

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

Mitte, who, like his character Walter “Flynn” White Jr., had cerebral palsy, played an integral supporting role on the AMC series, which premiered in 2008 and lasted five seasons.

From Los Angeles Times ● Oct. 12, 2026

How do Facebook, Instagram and all of Zuck’s other spawn remain integral parts of our lives until we die if users eventually get weary enough to figure out their existence is better off without them?

From Salon ● Oct. 11, 2026

“It’s an integral story to British identity. That’s why people feel an emotional attachment to it,” said Daisy Dixon, a philosophy of art lecturer at the University of Cardiff.

From The Wall Street Journal ● Oct. 4, 2026

It reaffirmed its "full solidarity" with Riyadh and said the kingdom's security was an integral part of Gulf security.

From Barron's ● Oct. 2, 2026

“We’re sorry for frightening you, Tris,” another voice says, “but anonymity is integral to our operation. We mean you no harm.”

From "Allegiant" by Veronica Roth

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

Calculations involving proton vibrational wavefunction overlap integrals supported this interpretation.

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

Liu and Ma then invoke a second old theorem that allows them to write the derivative of each master integral as a linear combination of the same 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

Random Word

Spin the wheel and learn a new word!

---

Related Words

• elemental
• essential
• indispensable
• intrinsic

---