Etymology
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integrate (v.)

1630s, "to render (something) whole, bring together the parts of," from Latin integratus, past participle of integrare "make whole," from integer "whole, complete," figuratively, "untainted, upright," literally "untouched," from in- "not" (see in- (1)) + root of tangere "to touch," from PIE root *tag- "to touch, handle."

The meaning "put together parts or elements and combine them into a whole" is from 1802. The "racially desegregate" sense (1940) probably is a back-formation from integration. Related: Integrated; integrating.

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Definitions of integrate

integrate (v.)
make into a whole or make part of a whole;
Synonyms: incorporate
integrate (v.)
open (a place) to members of all races and ethnic groups;
Synonyms: desegregate / mix
integrate (v.)
become one; become integrated;
The students at this school integrate immediately, despite their different backgrounds
integrate (v.)
calculate the integral of; calculate by integration;
From wordnet.princeton.edu