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

  • question_answer
    The value of \[\int_{\,-2}^{\,2}{\left[ p\ln \left( \frac{1+x}{1-x} \right)+q\ln {{\left( \frac{1-x}{1+x} \right)}^{-2}}+r \right]\,dx}\] depends on                                            [Orissa JEE 2003]

    A)                 The value of p  

    B)                 The value of q

    C)                 The value of r   

    D)                 The value of p and q

    Correct Answer: C

    Solution :

               Since \[\log \left( \frac{1+x}{1-x} \right)\]is an odd function                    \[\therefore \int_{\,-2}^{\,2}{\left\{ p\log \left( \frac{1+x}{1-x} \right)+q\,\log \,{{\left( \frac{1-x}{1+x} \right)}^{-2}}+r \right\}\,dx}\]                                 \[=r\int_{\,-\,2}^{\,2}{\,dx}=4r.\]Hence depends on the value of r.


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