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JEE Main & Advanced AIEEE Solved Paper-2013

  • question_answer
    Statement − I: The value of the integral\[\int\limits_{\pi /6}^{\pi /3}{\frac{dx}{1+\sqrt{\tan x}}}\]is equal to \[\frac{\pi }{6}\] Statement − II: \[\int\limits_{a}^{b}{f(x)dx}\int\limits_{a}^{b}{f(a+b-x)dx}\]     AIEEE Solevd Paper-2013

    A) Statement − I is true; Statement − II is true; Statement − II is a correct explanation for Statement − I.

    B) Statement − I is true; Statement − II is true; Statement − II is a not a correct explanation for Statement − I.

    C) Statement − I is true; Statement − II is false.

    D) Statement − I is false; Statement − II is true.

    Correct Answer: D

    Solution :

    \[I=\int\limits_{\pi /6}^{\pi /3}{\frac{dx}{1+\sqrt{\tan x}}}\]                        ? (i) \[I=\int\limits_{\pi /6}^{\pi /3}{\frac{dx}{1+\sqrt{\cot x}}}\]                        ? (ii) Adding (i) and (ii) \[\Rightarrow \]\[2I=\int\limits_{\lambda /6}^{\pi /3}{1dx}\]                      \[\Rightarrow \]\[2I=\frac{\pi }{3}-\frac{\pi }{6}\] \[2I=\frac{\pi }{6}\]                         \[\Rightarrow \]\[I=\frac{\pi }{12}\]


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