## Integral Sentence Examples

- It might be trivial, but it was an
**integral**part of their marriage. - - The range and importance of the scientific labours of Archimedes will be best understood from a brief account of those writings which have come down to us; and it need only be added that his greatest work was in geometry, where he so extended the method of exhaustion as originated by Eudoxus, and followed by Euclid, that it became in his hands, though purely geometrical in form, actually equivalent in several cases to integration, as expounded in the first chapters of our text-books on the
**integral**calculus. - Bright colours (especially red) are frequent, and the white chemise is an
**integral**part of the dress. - Peacock powerfully aided the movement by publishing in 1820 A Collection of Examples of the Application of the Differential and
**Integral**Calculus. - In 1548 Charles laid before the states a scheme for making the Netherlands an
**integral**part of the empire under the name of the Circle of Burgundy; but the refusal of the German Electors to make his only son Philip king of the Romans led him to abandon the project, which was never renewed. - The chronicler Saxo Grammaticus mentions in his Gesta Danorum the "rampart of Jutland" (Jutiae moenia) as having been once more extended by Valdemar the Great (1157-1182), which has been cited among the proofs that Schleswig (S4 nderjylland) forms an
**integral**part of Jutland (Manuel hist. - In 1746 and 1748 he published in the Memoirs of the Academy of Berlin "Recherches sur le calcul
**integral**," a branch of mathematical science which is greatly indebted to him. - This latter work included the differential and
**integral**calculus, the calculus of variations, the theory of attractions, and analytical mechanics. - The critical examination of the nature and growth of this compilation has removed much that had formerly caused insuperable difficulties and had quite unnecessarily been made an
**integral**or a relevant part of practical religion. - 1912 he made a daring incursion into Ulster, in order to advocate Home Rule at Belfast; but he was wise enough to give up his original intention of making the Ulster Hall, with its Orange and Protestant associations, the scene of his meeting, and also to represent the Government plan as an
**integral**part of parliamentary devolution. - For about a century the possession of this marchland was disputed by Hungary, Poland and Bohemia, but in 1029 it was finally incorporated with Bohemia, and so became an
**integral**part of the German empire.. - N be permuted, is a rational
**integral**symmetric function of the quantities. - All symmetric functions are expressible in terms of the quantities ap g in a rational
**integral**form; from this property they are termed elementary functions; further they are said to be single-unitary since each part of the partition denoting ap q involves but a single unit. - Associated Forms.-A system of forms, such that every form appertaining to the binary form is expressible as a rational and
**integral**function of the members of the system, is difficult to obtain. - If, however, we specify that all forms are to be rational, but not necessarily
**integral**functions, a new system of forms arises which is easily obtainable. - Of any form az there exists a finite number of invariants and covariants, in terms of which all other covariants are rational and
**integral**functions (cf. - The discriminant is the resultant of ax and ax and of degree 8 in the coefficients; since it is a rational and
**integral**function of the fundamental invariants it is expressible as a linear function of A 2 and B; it is independent of C, and is therefore unaltered when C vanishes; we may therefore take f in the canonical form 6R 4 f = BS5+5BS4p-4A2p5. - It filled her whole soul, had become an
**integral**part of herself, and she no longer struggled against it.