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In mathematics, the problem of differentiation of integrals is that of determining under what circumstances the mean value integral of a suitable function on a small neighbourhood of a point approximates the value of the function at that point. More formally, given a space X with a measure μ and a metric d, one asks for what functions f : X → R does
for all (or at least μ-almost all) x ∈ X? (Here, as in the rest of the article, Br(x) denotes the open ball in X with d-radius r and centre x.) This is a natural question to ask, especially in view of the heuristic construction of the Riemann integral, in which it is almost implicit that f(x) is a "good representative" for the values of f near x.
and 28 Related for: Differentiation of integrals information
In calculus, the Leibniz integral rule for differentiation under the integral sign states that for an integralof the form ∫ a ( x ) b ( x ) f ( x , t...
mathematics, the problem ofdifferentiationofintegrals is that of determining under what circumstances the mean value integralof a suitable function on...
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value of the integral. Mathematics portal Differentiation under the integral sign Telescoping series Fundamental theorem of calculus for line integrals Notation...
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path integral formulation of quantum mechanics actually refers not to path integrals in this sense but to functional integrals, that is, integrals over...
repeating of partial integration, because the RHS-integral vanishes. In the course of the above repetition of partial integrations the integrals ∫ u ( 0...
logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic derivative of a function...
integral is an integral whose unusual properties were first presented by mathematicians David Borwein and Jonathan Borwein in 2001. Borwein integrals...
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of finding a derivative is called differentiation. There are multiple different notations for differentiation, two of the most commonly used being Leibniz...
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