Problem 3714

Problems in Mathematical Analysis · 7.1

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Problem 3714

Let the function f(x)f(x) be continuous on the closed interval [a,A]\left[a,A\right]. Prove that

lim⁡h→+01h∫ax[f(t+h)−f(t)] dt=f(x)−f(a)(a<x<A). \lim _{h \to +0}\dfrac {1}{h}\int _{a}^{x}\left[f(t+h)-f(t)\right]\, dt=f(x)-f(a) \quad (a<x<A) .
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Problem 3714.1
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