What does integral mean?
Integral is an English word with both a general and a technical meaning. In everyday and formal prose, it describes something that is essential to the completeness or success of a larger thing: trust may be integral to friendship, or careful planning may be integral to a project. In this use, the word is more emphatic and formal than helpful or useful, suggesting that the named quality or feature cannot be removed without fundamentally changing the whole. In mathematics, an integral is a quantity representing the accumulated total of continuously varying values. It is commonly used to calculate the area under a curve, and it forms the basis of integral calculus. The word also has an adjective sense meaning complete or entire in specialist mathematical contexts. Historically, integral comes from Latin, where it meant whole or entire. This origin connects it with integer, integrity, and integrate, reflecting a shared idea of parts making up a complete whole.
Essential or necessary to the completeness, integrity, or success of something.
"The feedback of users was integral to improving the service."
Formal and standard in professional, academic, and explanatory prose.
In mathematics, a quantity representing the sum or accumulation of continuously varying values, especially the area under a curve.
"The definite integral gives the signed area under the curve over a specified interval."
Usually used in technical mathematical writing; the plural is integrals.
The plural is used for mathematical integrals, as in a discussion of definite and indefinite integrals.
"The two integrals combine to give the total area."
Integral hides a mathematical double life: it can describe something essential to a whole, or be the whole represented by a curve’s accumulated area.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does integral come from?
Integral comes through Middle English from Latin integralis, meaning “whole” or “entire,” and is related to integer, meaning “untouched” or “whole.” The Latin root integr- also underlies English words such as integrity, integrate, and integration. The mathematical noun uses the same idea of a whole quantity: an integral expresses the combined result of infinitely many small amounts. Its modern sense in calculus developed through the mathematical terminology associated with the same Latin root.
Related word forms
How integral is actually used
The adjective is common in formal and professional writing, where it means essential, indispensable, or central. In mathematics, the noun is usually encountered with terms such as definite, indefinite, and integral calculus.
Easily confused with integral
An integer is a whole number, whereas an integral is something essential to a larger whole or, in mathematics, a quantity expressing a sum or area.