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Nonstandard calculus
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infinitesimal h is suitably restricted. For the second theorem, the Riemann integral is defined as the limit, if it exists, of a directed family of RiemannCarus Mathematical Monographs (734 words) [view diff] case mismatch in snippet view article find links to article
Problems, by Charles Robert Hadlock - ISBN 9780883850206 The Generalized Riemann Integral, by Robert M. McLeod - ISBN 9780883850213 (out of print) From Error-CorrectingLobachevsky integral formula (427 words) [view diff] exact match in snippet view article find links to article
_{0}^{\infty }{\frac {\sin x}{x}}f(x)\,dx} is taken to be an improper Riemann integral, we have Lobachevsky's Dirichlet integral formula ∫ 0 ∞ sin 2 x xOscillation (mathematics) (1,146 words) [view diff] case mismatch in snippet view article
Trench, 3.5 "A More Advanced Look at the Existence of the Proper Riemann Integral", pp. 171–177 Hewitt and Stromberg (1965). Real and abstract analysisThe Analyst (2,061 words) [view diff] case mismatch in snippet view article find links to article
1986), "What is a Differential? A New Answer from the Generalized Riemann Integral", The American Mathematical Monthly, 93 (5): 348–356, doi:10.2307/2323591Hidegorō Nakano (407 words) [view diff] exact match in snippet view article find links to article
Riesz spaces, Orlicz-Nakano spaces and Nakano space. Source From Riemann integral to Lebesgue integral (1940) Hilbert Space Theory (1946) Classical IntegrationConvenient vector space (4,008 words) [view diff] no match in snippet view article find links to article
∞ ( R , E ) {\displaystyle c\in C^{\infty }(\mathbb {R} ,E)} the (Riemann-) integral ∫ 0 1 c ( t ) d t {\displaystyle \int _{0}^{1}c(t)\,dt} exists inVariance (10,185 words) [view diff] exact match in snippet view article find links to article
}^{+\infty }x^{2}f(x)\,dx-\mu ^{2},} where the integral is an improper Riemann integral. The exponential distribution with parameter λ is a continuous distributionList of inventions in the medieval Islamic world (9,274 words) [view diff] case mismatch in snippet view article find links to article
work by Al-Karaji, quoted by Al-Samaw'al in his "al-Bahir". Cauchy-Riemann Integral: Ibn al-Haytham gave a simple form of this. Decimal fractions: DecimalMultilinear form (4,599 words) [view diff] exact match in snippet view article find links to article
its integral over the unit n {\displaystyle n} -cell as the iterated Riemann integral of f {\displaystyle f} : ∫ [ 0 , 1 ] n ω = ∫ [ 0 , 1 ] n f d x 1 ∧Creep and shrinkage of concrete (4,305 words) [view diff] no match in snippet view article find links to article
(t')=[{\mbox{d}}\sigma (t')/{\mbox{d}}t']{\mbox{d}}t'} to obtain the standard (Riemann) integral. When history ϵ ( t ) {\displaystyle \epsilon (t)} is prescribed,