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

  • question_answer
    \[\int_{\,-2}^{\,2}{|x|\,dx=}\]                                   [MP PET 2000]

    A)                 0             

    B)                 1

    C)                 2             

    D)                 4

    Correct Answer: D

    Solution :

               \[I=\int_{-2}^{2}{|x|dx}\]\[=-\int_{-2}^{0}{x\,dx+\int_{0}^{2}{x\,dx}}\]\[=-\left[ \frac{{{x}^{2}}}{2} \right]_{-2}^{0}+\left[ \frac{{{x}^{2}}}{2} \right]_{0}^{2}\]                    \[=-(-2)+(2)=4\].


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