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Unit 3: Differentiation of an Integral
3.4 Review Questions Notes
x
1. If f is an integrable function on [a, b] and if F (x) = f(t) dt F(a) then check whether
a
F (x) = f (x) is absolute continuous function in [a, b] or not.
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2. If F is an absolutely continuous function on [a, b], then prove that F (x) = f(t) dt C where
a
f = F a.e. on [a, b] and C is constant.
3.5 Further Readings
Books Flanders, Harley. Differentiation under the Integral Sign
Frederick S. Woods, Advanced Calculus, Ginn and Company
David V. Widder, Advanced Calculus, Dover Publications Inc., New Edition
(Jul 1990).
Online links www.physicsforums.com > Mathematics > Calculus & Analysis
www.sp.phy.cam.ac.uk/~ alt 36/partial diff.pdf
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