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J & K CET Engineering J and K - CET Engineering Solved Paper-2004

  • question_answer
    The value of \[\int_{0}^{\pi /2}{\log \,\,\tan \,x\,\,dx}\] is

    A)  \[\frac{\pi }{8}\]

    B)  \[\infty \]

    C)  \[1\]

    D)  \[0\]

    Correct Answer: D

    Solution :

    Let \[I=\int_{0}^{\pi /2}{\log }\,\tan \,x\,dx\] ?.(i) \[\therefore \] \[I=\int_{0}^{\pi /2}{\log \,\,\tan \,\left( \frac{\pi }{2}-x \right)}\,\,dx\] \[\Rightarrow \] \[I=\int_{0}^{\pi /2}{\log \,1\,dx}\] \[\Rightarrow \] \[I=0\]


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