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

  • question_answer
    \[\int_{-1}^{1}{\log \frac{2-x}{2+x}\,dx}=\]   [Roorkee 1986; Kurukshetra CEE 1998]

    A)                 2             

    B)                 1

    C)                 \[-1\]    

    D)                 0

    Correct Answer: D

    Solution :

               Let \[f(x)=\log \left( \frac{2-x}{2+x} \right)\]                    \[\Rightarrow f(-x)=\log {{\left( \frac{2-x}{2+x} \right)}^{-1}}=-\log \left( \frac{2-x}{2+x} \right)=-f(x)\]                                 \[\therefore \] \[\int_{-1}^{1}{\log \left( \frac{2-x}{2+x} \right)\,\,dx=0}\]. 


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