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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 30

  • question_answer
    \[\int\limits_{0}^{\pi /2}{\frac{2\sqrt{\cos \theta }}{3(\sqrt{\sin \theta }+\sqrt{\cos \theta })}d\theta =}\]

    A) \[\pi /2\]            

    B) \[\pi /6\]

    C) \[\pi /3\]            

    D) \[\pi /4\]

    Correct Answer: B

    Solution :

    [b]: Let\[I=\int\limits_{0}^{\pi /2}{\frac{2\sqrt{\cos \theta }}{3\left( \sqrt{\sin \theta }+\sqrt{\cos \theta } \right)}d\theta }\] \[\therefore \]\[\frac{3}{2}I=\int\limits_{0}^{\pi /2}{\frac{\sqrt{\cos \theta }}{\left( \sqrt{\sin \theta }+\sqrt{\cos \theta } \right)}d\theta }\]                       ?(i) \[\frac{3}{2}I=\int\limits_{0}^{\pi /2}{\frac{\sqrt{\sin \theta }}{\left( \sqrt{\cos \theta }+\sqrt{\sin \theta } \right)}d\theta }\] Adding (i) and (ii), we get \[3I=\int\limits_{0}^{\pi /2}{d\theta =\frac{\pi }{2}}\] \[\Rightarrow \]\[I=\pi /6\]


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