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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 35

  • question_answer
    The slope of tangent drawn to the curve \[f(x)=\sin x-\int\limits_{0}^{x}{(x-t)\,f(t)}dt\]at \[x=0\]is equal to

    A) \[-1\]                     

    B)       \[0\]                       

    C) \[1\]         

    D)        \[2\]

    Correct Answer: C

    Solution :

    [c] \[f(x)=\sin x-\int\limits_{0}^{x}{(x-t)f(t)dt}\] \[=\sin x-x\int\limits_{0}^{x}{f(t)\,dt+}\int\limits_{0}^{x}{tf\,(t)\,dt}\] \[\therefore \,\,\,f'(x)=\cos x-xf(x)-\int\limits_{0}^{x}{f(t)\,dt+xf(x)}\] \[=\cos x-\int\limits_{0}^{x}{f(t)dt}\] \[\therefore \,\,\,g'(0)=1\]             


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