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

  • question_answer
    \[\int_{\,0}^{\,2}{\,|x-1|\,dx=}\]   [SCRA 1990; RPET 2001; UPSEAT 2003]

    A)                 0

    B)                 2

    C)                 1/2        

    D)                 1

    Correct Answer: D

    Solution :

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


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