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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2011

  • question_answer
    The value of \[\int_{0}^{4}{|x-1|}\,dx\]is

    A)  \[\frac{5}{2}\]                                  

    B)  5

    C)  4                                            

    D)  1

    Correct Answer: B

    Solution :

    \[\int_{0}^{4}{|x-1|dx=\int_{0}^{1}{-(x-1)dx+\int_{1}^{4}{(x-1)dx}}}\] \[=-\left[ \frac{{{x}^{2}}}{2}-x \right]_{0}^{1}+\left[ \frac{{{x}^{2}}}{2}-x \right]_{1}^{4}\] \[=-[1/2-1]+[8-4-1/2+1]\] \[=-(-1/2)+(4+1/2)\] \[=1/2+9/2\] \[=5\]


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