Let f be a continuous function [a, b] such that f(x)>0 for all x∈[a,b]. If F(x)=∫ax f(t)dt then

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F is differentiable but not increasing on [a, b]

F is differentiable and increasing on [a, b]

F is continuous and decreasing on [a, b]

F is neither differentiable nor increasing on [a, b]

answer is B.

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Detailed Solution

F′(x)=f(x)>0⇒ F is differentiable and increasing on [a, b].

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