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

  • question_answer
    \[\int_{-\frac{1}{2}}^{\,\frac{1}{2}}{\cos x\,\ln \frac{1+x}{1-x}dx}\] is equal to                     [AMU 2000]

    A)                 0             

    B)                 1

    C)                 2             

    D)                 ln 3

    Correct Answer: A

    Solution :

               \[I=\int_{-1/2}^{1/2}{\cos x\ln \left( \frac{1+x}{1-x} \right)\,dx}\]            \[\cos x\ln \left( \frac{1+x}{1-x} \right)\] is an odd function,  \[(\because \]\[f(-x)=-f(x)\])                                 \ \[I=0\].


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