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

  • question_answer
    \[\int_{\,-1}^{\,2}{|x|\,dx}\]                                      [DCE 1999]

    A)                 5/2        

    B)                 1/2

    C)                 3/2        

    D)                 7/2

    Correct Answer: A

    Solution :

     \[I=\int_{-1}^{2}{\,|x|dx}\]\[=\int_{-1}^{0}{-x\,dx}+\int_{0}^{2}{x\,\,dx}\]\[=-\left[ \frac{{{x}^{2}}}{2} \right]_{-1}^{0}+\left[ \frac{{{x}^{2}}}{2} \right]_{0}^{2}\]                  \[=-\left[ 0-\frac{1}{2} \right]+[2]\]\[=2+\frac{1}{2}=\frac{5}{2}\].


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