Etymology
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integral (adj.)

late 15c., "of or pertaining to a whole; intrinsic, belonging as a part to a whole," from Old French intégral (14c.), from Medieval Latin integralis "forming a whole," from Latin integer "whole" (see integer). Related: Integrally. As a noun, 1610s, from the adjective.

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Leibnitz 
Gottfried Wilhelm Leibnitz (also Leibniz), 1646-1716, German philosopher and mathematician, independent inventor (Newton was the other) of differential and integral calculus.
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built (adj.)

1560s, "constructed, erected," past-participle adjective from build (v.). Meaning "physically well-developed" is by 1940s (well-built in reference to a woman is from 1871); Built-in (adj.) "constructed as an integral part of a larger unit" is from 1895.

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reintegrate (v.)

c. 1600, "renew with regard to any state or quality," from re- "back," here "to a former condition," + integrate (v.). The sense of "make whole again, bring back to an integral condition" is from 1620s. The classically correct form is redintegrate (early 15c.). Earlier in a now-obsolete sense of "reinstate oneself" (1580s). Related: Reintegrated; reintegrating; reintegration.

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mantissa (n.)

"decimal part of a logarithm," 1865, from Latin mantisa "a worthless addition, makeweight," perhaps a Gaulish word introduced into Latin via Etruscan (compare Old Irish meit, Welsh maint "size"). So called as being "additional" to the characteristic or integral part. The Latin word was used in 17c. English in the sense of "an addition of small importance to a literary work, etc."

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broken (adj.)

"separated by force into parts, not integral or entire," past-participle adjective from Old English brocken, past participle of break (v.). Of terrain, "rough," 1590s; of language, "imperfect, ungrammatical," 1590s. Related: Brokenly; brokenness. Broken home, one in which the parents of children no longer live together, is from 1846. Broken record in reference to someone continually repeating the same thing is from 1944, in reference to scratches on phonograph disks that cause the needle to jump back and repeat.

When Britain's Minister of State, Selwyn Lloyd[,] became bored with a speech by Russia's Andrei Vishinsky in UN debate, he borrowed a Dizzy Gillespie bebop expression and commented: "Dig that broken record." While most translators pondered the meaning, a man who takes English and puts it into Chinese gave this translation: "Recover the phonograph record which you have discarded." [Jet, Oct. 15, 1953]
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member (n.)

c. 1300, "body part or organ, an integral part of an animal body having a distinct function" (in plural, "the body"), from Old French membre "part, portion; topic, subject; limb, member of the body; member" (of a group, etc.)," 11c., from Latin membrum "limb, member of the body, part," probably from PIE *mems-ro, from root *mems- "flesh, meat" (source also of Sanskrit mamsam "flesh;" Greek meninx "membrane," mēros "thigh" (the "fleshy part"); Gothic mimz "flesh").

In common use, "one of the limbs or extremities." Especially "the sex organ" (c. 1300, compare Latin membrum virile, but in English originally of women as well as men). Figurative sense of "anything likened to a part of the body" is by 14c., hence "a component part of any aggregate or whole, constituent part of a complex structure, one of a number of associated parts or entities."

The transferred sense of "person belonging to a group" is attested from mid-14c., from notion of "person considered in relation to an aggregate of individuals to which he or she belongs," especially one who has united with or been formally chosen as a corporate part of an association or public body. This meaning was reinforced by, if not directly from, the use of member in Christian theology and discourse from mid-14c. for "a Christian" (a "member" of the Church as the "Body of Christ"). Meaning "one who has been elected to parliament" is from early 15c.

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