Let f:(-1, 1)→R be a continuous function. If ∫sin x 0 f(t)dt = √32x, then f(√3/2) is equal to

∫sin x 0 f(t)dt = √32x
Differentiating using Leibniz rule,
f(sin x).cos x = √3/2
Putting x = π/6 we get,
f(√3/2). (1/2) = √3/2
∴ f(√3/2) = √3