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

  • question_answer
    If \[f(x)=|x-1|\], then \[\int_{0}^{2}{f(x)dx}\]is                 [Orissa JEE 2004]

    A)                 1             

    B)                 0

    C)                 2             

    D)                 ?2

    Correct Answer: A

    Solution :

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


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