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JEE Main & Advanced Sample Paper JEE Main Sample Paper-21

  • question_answer
    Let \[f:\text{ }R\to R\] be a differentiable function and \[f(1)=10.\]Then the value of \[\underset{x\to I}{\mathop{\lim }}\,\int\limits_{10}^{f(x)}{\frac{2t}{x-1}}\]  equals

    A)  2f'(1)                           

    B)  8f'(1)

    C)  10f'(1)             

    D)  20f'(1)

    Correct Answer: D

    Solution :

    \[\underset{x\to 1}{\mathop{Lim}}\,\,\frac{\int\limits_{10}^{f(x)}{2tdt}}{x-1}\,\,\,\,\,\,\,\,\left( \frac{0}{0} \right)\]            \[=2f(1)\times f'(1)\,=20f'(1)\]


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