| 单词 | definite integral |
| 释义 | > as lemmasdefinite integral 4. Mathematics (a) (Of a function): That quantity of which the given function is the differential or differential coefficient (corresponding to the fluent of a given fluxion in Newton's method); so called because it may be regarded as the whole sum of a series of consecutive values assumed by an infinitesimal function (differential) of the variable while the latter changes continuously from any one value to any other. When such limits of variation are fixed or determinate, it is called a definite integral: see quot. 1877. An integral is denoted by the sign ∫ (originally a long s, for Latin summa sum); in a definite integral the inferior and superior limits are indicated at the bottom and top of the sign, thus ∫ba. (Formerly sometimes applied to the quantity from which a given ‘finite difference’ or ‘increment’ is derived, as in quot. 1763; cf. quot. 1832 at integrate v. 3a.) (b) (Of a differential equation, or a system of such equations): An equation or system of equations from which the given equation or system can be derived by differentiation. (In relation to a system of equations, any quantity which that system makes constant is sometimes called its integral.) ΘΚΠ the world > relative properties > number > calculus > [noun] > integral calculus > integration or integrability > integral fluent1706 integral1728 gamma function1834 surface integral1867 Riemann integral1894 Cauchy's integral1898 Lebesgue integral1905 Stieltjes integral1914 convolution1934 1728 E. Chambers Cycl. at Calculus ∫ydx will denote the Sum, or Integral of the Differential ydx. 1763 W. Emerson Method of Increments Pref. p. vii Some Increments have no integrals, but what infinite series afford. 1802 Woodhouse in Philos. Trans. (Royal Soc.) 92 90 The integral or fluent of Px· is that function from which Px· is derived. 1877 B. Williamson Elem. Treat. Integral Calculus (ed. 3) vi. §91 The expression ∫X/ x0 ϕ(x)dx is called the definite integral of ϕ(x)dx between the limits x0 and X, and represents the limit of the sum of the infinitely small elements ϕ(x)dx, taken between the proposed limits... In contradistinction, the name indefinite integrals is often applied to integrals..in which the form of the function is merely taken into account, without regard to any assigned limits. 1881 J. C. Maxwell Treat. Electr. & Magnetism (ed. 2) I. 27 The double integrals destroy each other. < as lemmas |
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