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[ad. L. integr{amac}ti{omac}n-em (in L. only in sense ‘renewal, restoration to wholeness’), n. of action from integr{amac}re to INTEGRATE. Cf. mod.F. intégration (1700 in Hatz.-Darm.).]

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The action or process of integrating.

  • 1. a. The making up or compostion of a whole by adding together or combining the separate parts or elements; combination into an integral whole: a making whole or entire. (Often opposed to differentiation; sometimes with allusion to sense 2.)

1620 T. GRANGER Div. Logike 178 The Integrall in Logike..respecteth..integration whereby the totall is made a totall of all his members together. 1658 PHILLIPS, Integration, a making whole, or restoring. 1846 GROTE Greece I. xxi. II. 201 Their first permanent arrangement and integration was delayed for three centuries and accomplished at last only by the taste of Peisistratus. 1855 H. SPENCER Princ. Psychol. (1872) I. III. x. 376 Out of co-ordination, there grows up integration. 1873 G. HENSLOW Evol. Liv. Things x. 129 Physical conditions will ever give rise to differentiation in Beings, together with its concomitant phenomenon, integration.

b. Psychol. The combining of diverse parts into a complex whole; a complex state the parts of which are distinguishable; the harmonious combination of the different elements in a personality. Also attrib.

1855 H. SPENCER Princ. Psychol. III. xiv. 481 Progress in integration has been a necessary accompaniment of progress in speciality and complexity. 1893 J. M. BALDWIN Elem. Psychol. 36 Integration, therefore, represents a structural change in the direction both of simplicity and of complexity. 1931 Brit. Jrnl. Psychol. July 25 A more adequate psychological theory..speaks of the ‘integration’ of the constituent sensations into a perception. 1937 L. T. HOPKINS Integration i. 2 Integration must be the shorthand word to describe the process involved in this intelligent ongoing, interacting, adjusting behavior. 1938 L. P. THORPE Psychol. Found. Personality ix. 434 Perhaps we are warranted then in using the word integration with the understanding that it stands for a wholeness in personality which gives direction to the coordination of parts. 1943 H. READ Educ. through Art IV. iv. 81 Jaensch's next step is to relate his classification to the degree of integration which the individual establishes between his mental imagery and the external world. 1963 LANGNER & MICHAEL Life Stress & Mental Health xvi. 460 Integration involves the incorporation of the ‘thou shalt nots’ as well as the ‘thou shalts’, the acceptance of the middle-class rules of the game as well as the goal of winning.

c. The bringing into equal membership of a common society those groups or persons previously discriminated against on racial or cultural grounds.

1940 T. J. HAARHOFF S. Afr. & Crisis Mod. Civilization 19 For the great task that awaits us in South Africa is a task of integration, of making the Union into a unity. 1949 Jrnl. Racial Affairs I. I. 25 Although..assimilation would destroy the racial differences in South Africa, it would necessitate the prior integration of the cultures{em}a very difficult and uncertain process. Apart from that one argument, there is practically no other logical reason in support of either racial or cultural integration. 1951 J. D. L. KRUGER Bantustan: Study in Pract. Apartheid iii. 15 In fact it is difficult if not impossible to think of a single aspect of integration which could be regarded as beneficial to the white population. 1955 Ann. Amer. Acad. Pol. & Social Sci. CCCII. 25/1 The frontier for race relations has been shifting more and more to the housing field... The degree of integration in the schools now depends very largely on the residential pattern. 1968 Listener 26 Dec. 855/3, I define integration not as a flattening process of assimilation but as equal opportunity accompanied by cultural diversity in an atmosphere of mutual tolerance. 1970 Times 23 Mar. 13/3 It seemed that all we had to do to achieve integration was to sit down at enough lunch counters together.

  • 2. Math. The operation of finding the integral of a given function or equation (see INTEGRAL B. 4); the inverse of differentiation.

integration by parts: integration by means of the formula {integ}udv = uv - {integ}vdu, where u and v are any functions of the same variable. constant of integration: an arbitrary constant which must be added to get the complete expression for an integral. sign of integration: the sign {integ} denoting an integral (see INTEGRAL B. 4a).

1727-41 CHAMBERS Cycl. s.v. Calculus, The integration is known to be justly performed, if the quantity found..being differenced, produce that proposed to be summed. 1837 BREWSTER Magnet. 173 A fluxionary the integration of which the curve may be constructed. 1877 B. WILLIAMSON Int. Calc. (ed. 2) vi. §90 The process of integration may be regarded as that of finding the limit of the sum of the series of values of a differential f(x)dx, when x varies by indefinitely small increments from any one assigned value to another... For example, in seeking the area of a curve, we conceive it divided into an indefinite number of suitable elementary areas, of which we seek to determine the sum by a process of integration.

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