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If [f((sqrt(3))/2)] is [.] denotes the g...

If `[f((sqrt(3))/2)]` is [.] denotes the greatest integer function) 4 (b) 5 (c) 6 (d) `-7`

A

`4`

B

`5`

C

`6`

D

`-7`

Text Solution

Verified by Experts

The correct Answer is:
B
`int_(cosx)^(1)t^(2)f(t)dt=1-cosx`
Differentiating both sides w.r.t `x`, we get
`d/(dx) int_(cosx)^(1)t^(2)f(t)dt=d/(dx)(1-cosx)`
or `-cos^(2)x f(cosx)(-sinx)=sinx`
or `cos^(2)xf(cosx)sinx=sinx`
or `f(cosx)=1/(cos^(2)x)`
Now `f((sqrt(3))/4)` is attained when `cosx=(sqrt(3))/4`
`:.f((sqrt(3))/4)=16/3=5.33`
`[f((sqrt(3))/4)]=5`
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