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Let f be a continuous function [a, b] such that 

f(x)>0 for all x[a,b]. If F(x)=axf(t)dt then

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a
F is differentiable but not increasing on [a, b]
b
F is differentiable and increasing on [a, b]
c
F is continuous and decreasing on [a, b]
d
F is neither differentiable nor increasing on [a, b]

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detailed solution

Correct option is B

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


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