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

  • question_answer
    If \[[x]\] denotes the greatest integer less than or equal to \[x,\] then the value of the integral \[\int_{0}^{2}{{{x}^{2}}[x]\,dx}\] equals [Kurukshetra CEE 1996; Pb. CET 2001]

    A)                 5/3        

    B)                 7/3

    C)                 8/3        

    D)                 4/3

    Correct Answer: B

    Solution :

                    \[\int_{0}^{2}{{{x}^{2}}[x]dx=\int_{0}^{1}{{{x}^{2}}(0)dx+\int_{1}^{2}{{{x}^{2}}(1)dx=0+\left[ \frac{{{x}^{3}}}{3} \right]}_{1}^{2}=\frac{7}{3}}}\].


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