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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 2

  • question_answer
    The value of \[\int\limits_{2}^{4}{\{|x-2|+|x-3|\}dx}\]

    A) 1                     

    B) 2        

    C) 3                     

    D) 5

    Correct Answer: C

    Solution :

    \[\int\limits_{2}^{4}{\{|x-2|+|x-2|\}\,dx}\]
    \[\int\limits_{2}^{3}{\{(x-2)-(x-3)\}dx}+\int\limits_{3}^{4}{\{(x-2)+(x-3)\}dx}\]
    \[=\int\limits_{2}^{3}{dx}+\int\limits_{3}^{4}{(2x-5)dx=\left[ x \right]_{2}^{3}+\left[ \frac{2{{x}^{2}}}{2}-5x \right]_{3}^{4}}\]\[=(3-2)+[(16-20)-(9-15)]=1-4+6=3\]


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