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JEE Main & Advanced JEE Main Paper (Held On 11 April 2015)

  • question_answer
    Let \[f:(-1,1)\to R\] be a continuous function. If \[\int\limits_{0}^{\sin x}{f(t)dt}=\frac{\sqrt{3}}{2}x,\] then\[f\left( \frac{\sqrt{3}}{2} \right)\]is equal to : [JEE Main Online Paper (Held On 11 April 2015)]  

    A) \[\frac{\sqrt{3}}{2}\]

    B) \[\sqrt{3}\]

    C) \[\sqrt{\frac{3}{2}}\]

    D) \[\frac{1}{2}\]

    Correct Answer: B

    Solution :

      \[\int\limits_{0}^{\sin x}{f\left( x \right)}dx=\frac{\sqrt{3}}{2}x\] ? Differentiating both sides w.r.t.x \[f\left( \sin x \right)\cos x=\frac{\sqrt{3}}{2}\]\[x=\frac{\pi }{3}\] \[\Rightarrow \]\[y\left( \frac{\sqrt{3}}{2} \right)\times \frac{1}{2}=\frac{\sqrt{3}}{2}\]\[\Rightarrow \]\[f\left( \frac{\sqrt{3}}{2} \right)=\sqrt{3}\]


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