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JEE Main & Advanced Mathematics Definite Integration Question Bank Summation of series by Definite Integration, Gamma function, Leibnitz's rule

  • question_answer
    If \[f(x)=\int_{0}^{x}{t\sin t\,dt\,,}\] then \[{f}'(x)=\]                                 [MNR 1982; Karnataka CET 1999]

    A)                 \[\cos x+x\sin x\]            

    B)                 \[x\sin x\]

    C)                 \[x\cos x\]         

    D)                 None of these

    Correct Answer: B

    Solution :

                       Since,\[f(x)=\int_{0}^{x}{t\sin tdt}\].Now, according to Leibnitz's rule,                                 \[{f}'(x)=x\,\sin x.(1)-0=x\sin x\].


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