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JEE Main & Advanced Mathematics Definite Integration Question Bank Properties of Definite Integration

  • question_answer
    Find the value of \[\int_{\,0}^{\,9}{[\sqrt{x}+2]dx},\] where [.] is the greatest integer function                                  [UPSEAT 2002]

    A)                 31          

    B)                 22

    C)                 23          

    D)                 None of these

    Correct Answer: A

    Solution :

               \[\int_{\,0}^{\,9}{[\sqrt{x}+2]}\,dx\]\[=\int_{0}^{1}{2\,dx+\int_{1}^{4}{3\,dx+\int_{4}^{9}{4\,dx}}}\]                 \[=2+(12-3)+(36-16)\]\[=2+9+20=31\].


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