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

  • question_answer
    The value of \[\int_{1}^{5}{(|x-3|+|1-x|)\,dx}\] is           [IIT Screening]

    A)                 10          

    B)                 \[\frac{5}{6}\]

    C)                 21          

    D)                 12

    Correct Answer: D

    Solution :

                       \[\int_{1}^{5}{(|x-3|+|1-x|)dx}\]\[=\int_{1}^{5}{|x-3|dx+\int_{1}^{5}{|1-x|}\text{ }dx}\]                                       \[=\int_{1}^{3}{-(x-3)dx+\int_{3}^{5}{(x-3)}\,dx+}\int_{1}^{5}{-(1-x)\,}dx\]\[=12\].


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