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

In many Christian churches, donating, or “giving offerings,” is integral to earning respect and a sense of belonging from the congregation.

From Salon

A musician being filmed for a documentary wouldn’t want to alienate the fans that have been an integral part of their success, lest they risk damaging their brand.

From Salon

NHS Shetland is now advertising for the permanent job to replace her, describing it as "a unique opportunity to become an integral part of island life".

From BBC

Home Depots is particularly contentious because day laborers, primarily Latino men, have for decades represented an integral part of the Los Angeles labor force.

From Los Angeles Times

His dark complexion, rustic drawl and streetwise swagger became integral to his cinematic identity.

From BBC

Related Words

• elemental 
• essential 
• indispensable 
• intrinsic