An integral
...s of the form $F+C$, where $C$ is a constant. Consequently, the indefinite integral \eqref{*} consists of all functions of the form $F+C$.
2 KB (292 words) - 20:53, 1 January 2019
A generalization of the narrow [[Denjoy integral|Denjoy integral]] introduced by A.Ya. Khinchin in [[#References|[1]]].
...ywhere. Sometimes the Khinchin integral is also called the Denjoy–Khinchin integral.
1 KB (157 words) - 08:39, 23 July 2014
...n to another variable of integration. For the [[Definite integral|definite integral]] the formula is
...alogue of \eqref{e:change_of_var} for the [[Indefinite integral|indefinite integral]] is the assertion that, if $F$ is a primitive of $f$, then $F\circ \phi$ i
2 KB (308 words) - 14:34, 17 November 2012
...real numbers, while $m$, $n$ and $p$ are rational numbers. The indefinite integral of a differential binomial,
...bers $p$, $(m+1)/n$ and $p+(m+1)/n$ is an integer. In all other cases, the integral of a differential binomial cannot be expressed by elementary functions (P.L
712 bytes (119 words) - 20:23, 1 January 2019
...is an additive set function. If $F$ is continuous, the indefinite Burkill integral is continuous as well.
...The Burkill integral is used in constructing the [[Denjoy integral|Denjoy integral]] in different spaces.
3 KB (563 words) - 09:54, 27 November 2018
The indefinite integral of the binomial differential
426 bytes (73 words) - 21:00, 9 December 2014
A method for isolating the algebraic part in indefinite integrals of rational functions. Let $ P( x) $
...ration of a rational fraction whose denominator has only simple roots; the integral of such a fraction is expressed through transcendental functions: logarithm
3 KB (482 words) - 15:56, 2 March 2022
...he derivative of an elementary function is also elementary; the indefinite integral of an elementary function cannot always be expressed in terms of elementary
1 KB (146 words) - 15:13, 4 May 2012
Finding the [[Strong derivative|strong derivative]] of an indefinite integral
is summable on $G$ (in particular, if $f\in L_p(G)$, $p>1$), then the integral $F$ of $f$ is strongly differentiable almost-everywhere on $G$. For any $\p
2 KB (271 words) - 14:20, 14 February 2020
...which are arbitrarily close to its indefinite [[Lebesgue integral|Lebesgue integral]]. The notion of majorant and minorant can be generalized to the case of ad
...<TR><TD valign="top">[2]</TD> <TD valign="top"> S. Saks, "Theory of the integral" , Hafner (1952) (Translated from French)</TD></TR></table>
2 KB (302 words) - 10:06, 15 April 2014
$#C+1 = 154 : ~/encyclopedia/old_files/data/I051/I.0501360 Integral calculus
...with it constitutes the foundation of mathematical analysis. The origin of integral calculus goes back to the early period of development of mathematics and it
22 KB (3,436 words) - 22:12, 5 June 2020
$#C+1 = 125 : ~/encyclopedia/old_files/data/M065/M.0605370 Multiple integral
...multiple integral (Riemann integral, Lebesgue integral, Lebesgue–Stieltjes integral, etc.).
11 KB (1,648 words) - 16:53, 20 January 2024
...lated forms of the integral constitutes the problem of [[Integral calculus|integral calculus]].
...ral science and technology, the notions of the indefinite and the definite integral have undergone a number of generalizations and modifications.
14 KB (2,170 words) - 17:21, 14 February 2020
The indefinite integral of sine is:
...interval $[-1,1]$ by $\phi(x)=\int_0^xdt/\sqrt{1-t^2}$. For $x=\pm1$ this integral is improper, but convergent. It is easy to see that $\phi$ is monotone incr
3 KB (441 words) - 13:51, 14 February 2020
The indefinite integral of the secant is
1 KB (202 words) - 15:13, 14 February 2020
$#C+1 = 18 : ~/encyclopedia/old_files/data/S110/S.1100170 Skorokhod integral
...nsion of the Itô stochastic integral (cf. [[Stochastic integral|Stochastic integral]]) introduced by A.V. Skorokhod in [[#References|[a8]]] in order to integra
4 KB (612 words) - 08:14, 6 June 2020
...on $(-\infty,\infty)$, then $f'(x)$ is $U$-almost-periodic; the indefinite integral $F(x)=\int_0^xf(t)dt$ is $U$-almost-periodic if $F(x)$ is a bounded functio
2 KB (376 words) - 10:22, 24 August 2014
The indefinite integral of the tangent is:
1 KB (237 words) - 14:16, 14 February 2020
...e fundamental differences in the reduction theory of positive-definite and indefinite quadratic forms.
==The reduction of indefinite quadratic forms.==
19 KB (2,708 words) - 08:06, 14 January 2024
...op">[a1]</TD> <TD valign="top"> M.G. Krein, "Topics in differential and integral equations and operator theory" , Birkhäuser (1983) (Translated from Russ
..."> I. [I. Gokhberg] Gohberg, P. Lancaster, L. Rodman, "Matrices and indefinite scalar products" , Birkhäuser (1983)</TD></TR>
2 KB (348 words) - 19:54, 26 November 2016