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

  • question_answer
    \[\int_{\,-\,2}^{\,2}{\,\left| \,[x]\, \right|\,dx=}\]                                            [EAMCET 2003]

    A)                 1

    B)                 2

    C)                 3             

    D)                 4

    Correct Answer: D

    Solution :

     \[\int_{-2}^{2}{|[x]|}\,dx=\int_{\,-2}^{\,-1}{\,|[x]|dx+\int_{-1}^{0}{|[x]|dx+\int_{0}^{1}{|[x]|dx|+\int_{1}^{2}{|[x]|dx}}}}\]                        \[=\int_{-2}^{-1}{2dx\,\,}+\int_{-1}^{0}{1dx+\int_{0}^{1}{0\,dx+}}\int_{1}^{2}{1dx}\]                      \[=2[x]_{-2}^{-1}+[x]_{-1}^{0}+0+[x]_{1}^{2}\]                                   \[=2(-1+2)+(0+1)+(2-1)=2+1+1=4.\]


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