integral
UK[ˈɪntɪɡrəl]US[ˈɪn.t̬ə.ɡrəl]
adj
Necessary to make something whole or complete; forming an essential part.
adj
Of or denoted by an integer; relating to integers.
n
A function of which a given function is the derivative, i.e., which yields that function when differentiated, and which may express the area under the curve of a graph of the function.
Morpheme Breakdown
in
tegr
al
in
not
tegr
to touch.
al
Etymology
The word "integral" originates from the Late Latin integralis, meaning "forming a whole," which itself derives from the Latin integer, signifying "untouched, whole, entire." This Latin term is a compound of the intensive prefix in- and the root teg- (from tangere, "to touch"), thus conveying the literal idea of "not touched," and by extension, "complete, intact." The mathematical senses developed in the 17th and 18th centuries, logically extending from the core concept of wholeness: an integer is a whole number, and the integral calculus deals with the summation of parts to find a whole. Therefore, the modern abstract meanings of being essential for completeness or relating to a mathematical whole are direct descendants of this ancient notion of untouched integrity.
Analysis
Structure: in + tegr + al
- in- (Latin): A prefix meaning "not" or "without," but in this context, it acts as an intensive prefix meaning "thoroughly."
- tegr- (Latin): A root from the Latin verb tangere, meaning "to touch." Its past participle stem tact- led to "tactile," while its supine stem tag- and frequentative form tangitare evolved into integrum, meaning "untouched, whole, entire."
- -al (Latin): An adjectival suffix meaning "of, relating to, or characterized by."
Examples
Practice is an integral part of language learning.
The concept of sustainability is integral to the company's mission.
He solved the problem by calculating the definite integral.