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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Self Evaluation Test - Integrals

  • question_answer
    Find the value of \[\int\limits_{0}^{9}{[\sqrt{x}+2]dx}\] where \[[\cdot ]\] is the greatest integer function:

    A) 31

    B) 22

    C) 23

    D) None of these

    Correct Answer: A

    Solution :

    [a] We have \[\int\limits_{0}^{9}{[\sqrt{x}+2]dx}\] \[=\int\limits_{0}^{1}{2dx+\int\limits_{1}^{4}{3dx+\int\limits_{4}^{9}{4dx}}}\] \[=2+(12-3)+(36-16)=2+9+20=31\]


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