integral

[in-ti-gruhl, in-teg-ruhl]

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

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

/ 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

1. Involving or expressed as an integer or integers.

1. See definite integral indefinite integral

Other Word Forms

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

Word History and Origins

Origin of integral¹

From the Medieval Latin word integrālis, dating back to 1545–55. See integer, -al ¹

Example Sentences

Moody had a distinguished rugby union career - playing an integral role at flanker and coming off the bench to help England win the 2003 World Cup in Australia.

Read more on BBC

She was described by police as being integral part of the drugs ring.

Read more on BBC

Mahmood will argue that "fair migration" and secure borders are integral parts of an "open, generous, tolerant" country.

Read more on BBC

The crucifix was on wheels, because in modern-day America, an integral part of choosing your cross to bear is figuring out how to make it everyone else’s problem.

Read more on Salon

School district officials say they have not been told the circumstances of his arrest, and have called him an integral part of the school community.

Read more on BBC

Related Words

• elemental 
• essential 
• indispensable 
• intrinsic