integral

The word “integral” means essential to completeness; a necessary part of a whole. In plain terms, either "necessary/built-in" (everyday sense) or a calculus term for the area/total under a curve (maths sense).

“Integral” is pronounced IHN-tihgrl (/ˈɪntəɡɹəl/ in IPA).

Here is “integral” used in a sentence: “Trust is integral to any good working relationship.”

Depending on how it is used, “integral” can be an adjective and a noun.

The word “integral” comes from Latin. From Latin integer, "whole, untouched" — the same root as the number word "integer.".

“Integral” is a fairly common word in modern English, usually learned at around the C1 level.

“Integral” has 2 distinct senses listed in this dictionary. The most common is: essential to completeness; a necessary part of a whole.

Integral, as an adjective, means essential to completeness, a necessary part of a whole. Integrated means combined or brought together into a unified whole. Something integral is required for the whole to be complete, while something integrated has been merged into it.

Both mean necessary, but integral stresses being a built-in, inseparable part of a larger whole, while essential stresses being absolutely required. They are close synonyms and often interchangeable.

Both are correct. You can say something is "integral to" a system, where a noun follows, or that it is "an integral part of" it, which is a common fixed phrase. Both express that the thing is essential to the whole.

In calculus, an integral finds the area under a curve or a function's total accumulated value, while a derivative finds the rate at which a function is changing. They are inverse operations of each other.