JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Rolle's theorem Lagrange's mean value theorem

  • question_answer
    If \[f(x)\] satisfies the conditions of Rolle?s theorem in \[[1,\,2]\] and \[f(x)\] is continuous in \[[1,\,2]\] then \[\int_{1}^{2}{f'(x)dx}\] is equal to                                                               [DCE 2002]

    A)            3

    B)            0

    C)            1

    D)            2

    Correct Answer: B

    Solution :

               \[\int_{1}^{2}{{f}'(x)dx=[f(x)]_{1}^{2}}=f(2)-f(1)=0\] (\[\because \]\[f(x)\]satisfies the conditions of Rolle?s theorem, \ \[f(2)=f(1)]\]) .

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