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

  • question_answer
    The value of \[\int_{\,a}^{\,b}{\frac{x}{|x|}dx,\,\,a<b<0}\] is     [Orissa JEE 2003]

    A)                 \[-(|\,a\,|+|\,b\,|)\]    

    B)                 \[|b|-|a|\]

    C)                 \[|a|-|b|\]        

    D)                 \[|a|+|b|\]

    Correct Answer: B

    Solution :

               \[\int_{a}^{b}{\frac{x}{|x|}dx=-}\int_{a}^{b}{dx}\],    (\[\because \text{ }a<b<0\])            \[=-(b-a)=\,|b|-|a|\].


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