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Let f : (-1,1) to R be continous funct...

Let `f : (-1,1) to R ` be continous function , if ` int _(0)^(sinx) f(t) dt = (sqrt(3))/2 x , "then " f ((sqrt(3))/2 )` is equal to

A

`(1)/(2)`

B

`(sqrt3)/(2)`

C

`sqrt((3)/(2))`

D

`sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
D
Given , ` int _(0)^(sin x) f(t) dt = (sqrt(3))/2 x`
On differentiating w.r.t x , we get
`f(sin) cos x = (sqrt(3))/2 ` [ Using Leibnitz theorem ]
If ` sin x = (sqrt(3))/2 rArr x = pi/3 `
` :. f (sin pi/3) cos.pi/3 = (sqrt(3))/2 rArr f (sqrt(3)/2) . 1/2 = (sqrt(3))/2 `
` rArr f((sqrt(3))/2) = sqrt(3)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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