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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2008

  • question_answer
    \[\int_{-2}^{2}{|[x]|}dx\]is equal to

    A)  1                            

    B)         2

    C)  3                            

    D)         4

    E)  5

    Correct Answer: D

    Solution :

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


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