, one of an important class of integrals, occurring in the higher mathematics; — so called because one of the integrals expresses the length of an arc of an ellipse.

(In`te*gral"i*ty) n. [Cf. F. intégralité.] Entireness. [Obs.] Whitaker.

(In"te*gral*ly) adv. In an integral manner; wholly; completely; also, by integration.

(In"te*grant) a. [L. integrans, -antis, p. pr. of integrare to make whole, renew: cf. F. intégrant. See Integrate.] Making part of a whole; necessary to constitute an entire thing; integral. Boyle.

All these are integrant parts of the republic.

Integrant parts, or particles, of bodies, those smaller particles into which a body may be reduced without loss of its original constitution, as by mechanical division.

(In"te*grate) v. t. [imp. & p. p. Integrated ; p. pr. & vb. n. Integrating ] [L. integratus, p. p. of integrare to make whole, renew: cf. F. intégrer. See Integer, Entire.]

1. To form into one whole; to make entire; to complete; to renew; to restore; to perfect. "That conquest rounded and integrated the glorious empire." De Quincey.

Two distinct substances, the soul and body, go to compound and integrate the man.

2. To indicate the whole of; to give the sum or total of; as, an integrating anemometer, one that indicates or registers the entire action of the wind in a given time.

3. (Math.) To subject to the operation of integration; to find the integral of.

(In`te*gra"tion) n. [L. integratio a renewing, restoring: cf. F. intégration.]

1. The act or process of making whole or entire.

2. (Math.) The operation of finding the primitive function which has a given function for its differential coefficient. See Integral.

The symbol of integration is &integral2l (standing for the Latin summa sum), and the integral is also regarded as the limiting value of the sum of great numbers of differentials, when the magnitude of the differentials decreases, and their number increases indefinitely. See Limit, n. When the summation is made between specified values of the variable, the result is a definite integral, and those values of the variable are the limits of the integral. When the summation is made successively for two or more variables, the result is a multiple integral.

3. In the theory of evolution: The process by which the manifold is compacted into the relatively simple and permanent. It is supposed to alternate with differentiation as an agent in development.

(In"te*gra`tor) n. (Math. & Mech.) That which integrates; esp., an instrument by means of which the area of a figure can be measured directly, or its moment of inertia, or statical moment, etc., be determined.

(In*teg"ri*ty) n. [L. integritas: cf. F. intégrité. See Integer, and cf. Entirety.]

1. The state or quality of being entire or complete; wholeness; entireness; unbroken state; as, the integrity of an empire or territory. Sir T. More.

Elliptic integral

  By PanEris using Melati.

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