derivative of Riemann integral

Let f be a continuous functionMathworldPlanetmathPlanetmath from an open subset A of 2 to .  Suppose that also the partial derivativeMathworldPlanetmathft(x,t)  is continuous in A which contains the line segments along which the integration is performed and that a(t) and b(t) are real functions differentiableMathworldPlanetmathPlanetmath in some point t0.  Denote




Then one has the derivativePlanetmathPlanetmath


in all such points  t=t0.

Title derivative of Riemann integral
Canonical name DerivativeOfRiemannIntegral
Date of creation 2013-03-22 14:35:30
Last modified on 2013-03-22 14:35:30
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 9
Author PrimeFan (13766)
Entry type Theorem
Classification msc 26A24
Classification msc 26A42
Related topic DifferentiationUnderIntegralSign