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JEE Main 2015 · 11 Apr · Shift 1, Mathematics question 76

Let f:(−1,1)→Rf:(-1,1)\to\mathbb R be a continuous function. If ∫0sin⁡xf(t) dt=32x\displaystyle\int_0^{\sin x}f(t)\,dt=\frac{\sqrt3}2x, then f(32)f\left(\dfrac{\sqrt3}2\right) is equal to :

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Answer and worked solution

Official answer: B

Differentiating, f(sin⁡x)cos⁡x=32f(\sin x)\cos x=\frac{\sqrt3}2. At sin⁡x=32\sin x=\frac{\sqrt3}2, cos⁡x=12\cos x=\frac12, so f(32)=3f\left(\frac{\sqrt3}2\right)=\sqrt3.

Topics:Leibniz rule
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