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Ifint(sinx)^1t^2f(t)dt=1-sinx ,w h e r e...

`Ifint_(sinx)^1t^2f(t)dt=1-sinx ,w h e r e .x in (0,pi/2),` then find the value of `f(1/(sqrt(3)))dot`

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We have `int_(sinx)^(1)t^(2)f(t)dt=1-sinx`
Differentiating both side w.r.t `x`, we get
`1^(2)xxf(1)xx0-sin^(2)x xx f(sinx)xxcosx=-cosx`
`impliesf(sinx)=1/(sin^(2)x)`
`:.f(1/(sqrt(3)))=3`.
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