Noun
Riemann integral (plural Riemann integrals)
English Wikipedia has an article on:Riemann integralWikipedia
(mathematical analysis) A type of integral whose computation involves dividing the interval of integration into smaller sub-intervals, summing sample values of the integrand inside those sub-intervals multiplied by their lengths, and letting the number of sub-intervals tend to infinity.
A "proper" Riemann integral assumes the integrand is defined and finite on a closed and bounded interval, bracketed by the limits of integration. Source: Internet
As such, they have no Riemann integral. Source: Internet
Every continuous function : is integrable (for example in the sense of the Riemann integral ). Source: Internet
"Many functions in L 2 of Lebesgue measure, being unbounded, cannot be integrated with the classical Riemann integral. Source: Internet
But this is a fact that is beyond the reach of the Riemann integral. Source: Internet
However, many functions that can be obtained as limits are not Riemann-integrable, and so such limit theorems do not hold with the Riemann integral. Source: Internet