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

  • question_answer
    The function \[F(x)=\int_{0}^{x}{\log \left( \frac{1-x}{1+x} \right)}\,dx\] is

    A)                 An even function            

    B)                 An odd function

    C)                 A periodic function         

    D)                 None of these

    Correct Answer: A

    Solution :

                    We know that if \[f(t)\]is an odd function, then \[\int_{0}^{x}{f(t)}\] dt is an even function. since the function here \[f(x)=\log \frac{1-x}{1+x}\] is an odd function, therefore \[F(x)\]is an even function.


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