# Integration Sentence Examples

- The
**integration**can be effected without much difficulty. - But here he becomes hopelessly inconsistent, because he had already said, in defining it, that " evolution is an
**integration**of matter and concomitant dissipation of motion " (First Principles, § 145). - Accordingly, the optical distance from AoBo to A is represented by f (A +S/c)ds, the
**integration**being along the original path Ao. - In elliptic integrals, the amplitude is the limit of
**integration**when the integral is expressed in the form f 4) 1% I - N 2 sin e 4) d4. - The volume of the briquette for which u is a function of x and y is found by the operation of double
**integration**, consisting of two successive operations, one being with regard to x, and the other with regard to y; and these operations may (in the cases with which we are concerned) be performed in either order. - He published a memoir on the
**integration**of partial differential equations and a few others, which have not been noticed above, but they relate to subjects with which his name is not especially associated. - He supposes that evolution is primarily
**integration**, from the incoherent to the coherent, exemplified in the solar nebula evolving into the solar system; secondly differentiation, from the more homogeneous to the more heterogeneous, exemplified by the solar system evolving into different bodies; thirdly determination, from the indefinite to the definite, exemplified by the solar system with different bodies evolving into an order. - In addition, he wrote a number of scientific memoirs and papers, including two on the
**integration**of partial differential equations (Jour. - The
**integration**of the scattered tribes of Arabia in the 7th century by the stirring religious propaganda of Mahomet was accompanied by a meteoric rise in the intellectual powers of a hitherto obscure race. - By the principle of superposition the whole effect may be found by
**integration**of the partial effects due to each element of the surface, the other elements remaining at rest. - If the grating be composed of alternate transparent and opaque parts, the question may be treated by means of the general integrals (§ 3) by merely limiting the
**integration**to the transparent parts of the aperture. - (21) where the
**integration**extends throughout the whole space unoccupied by conductors. - We have by partial
**integration**ff1 fV dd - ' 2 dy JJ dx y JJ y dxd dz = V - d dzdxd dz, and Itwo (similar equations in y and z. - Since the change of energy is independent of the path, the finite change between any two given states may be found by
**integration**along any convenient path. - The direct
**integration**of this equation requires that L and v" - v' should be known as functions of p and 0, and cannot generally be performed. - Universally as an "
**integration**of matter and dissipation of motion," and yet mental, social and moral developments are also called evolution, so that, in accordance with the definition, they are alsoof matter and dissipations of motion.**integrations** - All that it is necessary to assume is that the effects of the successive zones gradually diminish, whether from the increasing obliquity of the secondary ray or because (on account of the limitation of the region of
**integration**) the zones become at last more and more incomplete. - 18), the nearest point on the wave-front, is wholly intercepted, and on the left the
**integration**is to be taken from s = CA to s = co. - The occurrence of factors such as sin 4), or 2 (1cos 0), in the expression of the secondary wave has no influence upon the result of the
**integration**, the effects of all the elements for which the factors differ appreciably from unity being destroyed by mutual interference. - The integral equation of continuity (I) may now be written l f fdxdydz+ff (lpu+mpv+npdso, (4) which becomes by Green's transformation (dt +d dz dy dx (p u) + d (p v) + d (p w) l I dxdydz - o, dp leading to the differential equation of continuity when the
**integration**is removed. - According to the assumed law of the secondary wave, the result must actually depend upon the precise radius of the outer boundary of the region of
**integration**, supposed to be exactly circular. - Next, he supposes that mind obeys the same law of evolution, and exemplifies
**integration**by generalization, differentiation by the development of the five senses, and determination by the development of the order of consciousness. - We have seen that the problem before us is independent of the law of the secondary wave as regards obliquity; but the result of the
**integration**necessarily involves the law of the intensity and phase of a secondary wave as a function of r, the distance from the origin. - A secondary wave suitable when the primary wave is undisturbed, with mere limitation of the
**integration**to the transparent parts of the screen. - The
may also be effected by means of polar coordinates, taking first the**integrations****integration**with respect to 4) so as to obtain the result for an infinitely thin annular aperture. - Only in this case can cos {p' +(m- -27th/Af) f } retain the constant value - I throughout the
**integration**, and then only when and a = 27Th/A f (8) cos p'=- 1 .. - (1), the effect at B is l abX 2 a+b - cos 2 T t f cos 27rv 2 .dv+sin 27t f sin27rv .dv (3), the limits of
**integration**depending upon the disposition of the diffracting edges. - 1, may be determined by direct
**integration**of (12), or from the observation that by their constitution G and H vanish when u= oo, coupled with the fact that C and S then assume the value 2. - The
**integration**of the several terms may then be effected by the formula e y dy =r(4+2)=(4 - i)(4-2)... - Cauchy, without the use of Gilbert's integrals, by direct
**integration**by parts. - For a point Q outside the shadow the
**integration**extends over more than half the primary wave. - It is then verified that, after
**integration**with respect to dS, (6) gives the same disturbance as if the primary wave had been supposed to pass on unbroken. - Here again, on
**integration**over the entire lamina, the aggregate effect of the secondary waves is necessarily the same as that of the primary. - At the same time provision must be made for the
**integration**of knowledge as well as for the winning of it by several adits. - A conspicuous example of the incalculable evil wrought by lack of
**integration**is well seen in the radical divorce of surgery from medicine, which is one of the most mischievous legacies of the middle ages - one whose mischief is scarcely yet fully recognized, and yet which is so deeply rooted in our institutions, in the United Kingdom at any rate, as to be hard to obliterate. - The processes which have to be performed in the mensuration of figures of this kind are in effect processes of
**integration**; the distinction between mensuration and**integration**lies in the different natures of the data. - The
**integration**with regard to y may similarly (in the particular example) be replaced by the operation ak(I+3E'-+3E'2+E'3), where E' denotes the change of y into y + k. - The European inhabitants live principally in the new town, which was gradually formed by the
**integration**of Weltevreden (Wellcontent), Molenvliet (Mill-stream), Rijswijk (Rice-town), Noordwijk (North-town), Koningsplein (King's square), and other suburban villages or stations. - In any region of velocity where it is possible to represent p with sufficient accuracy by an empirical formula composed of a single power of v, say v m, the
**integration**can be effected which replaces the summation in (to), (16), and (24); and from an analysis of the Krupp experiments Colonel Zabudski found the most appropriate index m in a region of velocity as given in the following table, and the corresponding value of gp, denoted by f (v)or v m lk or its equivalent Cr, where r is the retardation. - Lastly, when a theory of the world supposes a noumenal power, a resistent and persistent force, which results in an evolution, defined as an
**integration**of matter and a dissipation of motion, which having resulted in inorganic nature and organic nature, further results without break in consciousness, reason, society and morals, then such a theory will be construed as materialistically as that of Haeckel by the reader, whatever the intention of the author. - The study of evolution, without considering how many conditions are required for " the
**integration**of matter and the dissipation of motion " to begin, and the undoubted discoveries which have resulted from the study of inorganic and organic evolution, have led men to expect too much from this one law of Nature. - Proceeding on this suggestion, and misled by the mathematical expression which he had given to Weber's law, Fechner held that a conscious sensation, like its stimulus, consists of units, or elements, by summation and increments of which conscious sensations and their differences are produced; so that consciousness, according to this unnecessary assumption, emerges from an
**integration**of unconscious shocks or tremors. - Laplace owned that he had despaired of effecting the
**integration**of the differential equations relative to secular inequalities until Lagrange showed him the way. - On
**integration**and reduction. - 2n u (a -b.b -a')' not requiring the
**integration**of (II) and (12) If 0=a across the end J J' of the jet, where u = oo, q= Q, b-a' a-b ch 7/2,=cos na = I, , sh 162 = i sin na = i,, a - a a-a Then a-a'+(a+a) cos 2na-[a+a'+(a-a) cos 2najcos 2110 (a-a') sin' 2na X cos 211a - cos 2110 Along the wall AB, cos nO =o, sin n0= I, a> u> b, ch n2= i sh log (q) n= i? **Integration**of matter with concomitant dissipation of motion) and.- The
**integration**can be performed when M is expressed in terms of x. - F (q sec i)' from which the values of t, x, y, i, and tan i are given by
**integration**with respect to q, when sec i is given as a function of q by means of (51). - He finds that throughout the universe there is an unceasing redistribution of matter and motion, and that this redistribution constitutes evolution when there is a predominant
**integration**of matter and dissipation of motion, and constitutes dissolution where there is a predominant absorption of motion and disintegration of matter. - He also admits himself that mental evolution exemplifies
**integration**of matter and dissipation of motion only indirectly. - Journ., 18 43, 3, p. 46), determine the law of the secondary wave, by comparing the result of the
**integration**with that obtained by supposing the primary wave to pass on to P without resolution. - The limits of
**integration**for x may thus be taken to be -2a and -Fla, and for y to be -2b, +2b. - For a finite change it is necessary to represent the path by a series of small steps, which is the graphic equivalent of
**integration**along the path represented by the given relation between v and 0, or p and 0. - Taking 2 rv2 = u (9), we may write (17r oueiudu ?/ 2) u Again, by a known formula, 1 1 °° -1 uu = 1/ 7r?r o Substituting this in (to), and inverting the order of
**integration**, we get uc 2? - Of his philosophical doctrine proper, the most striking characteristic is
**Integration**, as opposed to Disintegration, both in thought and in reality. - Now taking equation (72), and replacing tan B, as a variable final tangent of an angle, by tan i or dyldx, (75) tan 4) - dam= C sec n [I(U) - I(u)], and integrating with respect to x over the arc considered, (76) x tan 4, - y = C sec n (U) - f :I(u)dx] 0 But f (u)dx= f 1(u) du = C cos n f x I (u) u du g f() =C cos n [A(U) - A(u)] in Siacci's notation; so that the altitude-function A must be calculated by summation from the finite difference AA, where (78) AA = I (u) 9 = I (u) or else by an
**integration**when it is legitimate to assume that f(v) =v m lk in an interval of velocity in which m may be supposed constant.