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

Example Sentences

How and why did pro football become such an integral part of the American experience?

From The Wall Street Journal

The Dalai Lama lives in exile in India and is known for his tireless campaign for greater autonomy for his Tibetan homeland, which Beijing says is an integral part of China.

From Barron's

The charismatic 90-year-old, who lives in exile in India, is lauded worldwide for his tireless campaign for greater autonomy for his Tibetan homeland, which Beijing says is an integral part of China.

From Barron's

The companies are also becoming an increasingly integral part of the effort to develop more advanced chips that enable improvements in AI.

From MarketWatch

What undermines Mr. Dalrymple’s thesis most, however, is the fact that no Indian leader believed Burma was an integral part of India—especially not Mahatma Gandhi.

From The Wall Street Journal

Related Words

• elemental
• essential
• indispensable
• intrinsic