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Let 'f is a function, continuous on [0,1...

Let 'f is a function, continuous on `[0,1]` such that `f(x) leq sqrt5 AA x in [0,1/2] and f(x) leq 2/x AA x in [1/2,1]` then smallest 'a' for which `int_0^1 f(x)dx leq a` holds for all 'f' is

Text Solution

Verified by Experts

The correct Answer is:
5
`f(x)` will be below `y=sqrt(5)` & `y=2/x`
`:.Ile int_(0)^(2//sqrt(5)) sqrt(5)dx+int_(2/(sqrt(5))) 2/x dx`
`=sqrt(5)(2/(sqrt(5)))+2 In 1-=2 In (2/(sqrt(5)))`
`=2+2 In ((sqrt(5))/2)`
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