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  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main Sample Paper-26

  • question_answer
    Let \[g(x)=\sqrt{{{\sin }^{-1}}(\cos ({{\tan }^{-1}}x))+{{\cos }^{-1}}(\sin ({{\cot }^{-1}}x))}\], then \[\int\limits_{-\sqrt{\frac{\pi }{2}}}^{\sqrt{\frac{\pi }{2}}}{g(x)dx}\] equals

    A)  0                    

    B)  \[\sqrt{\frac{\pi }{2}}\]

    C)  \[\frac{\pi }{2}\]                                   

    D)  \[\pi \]

    Correct Answer: B

    Solution :

    \[=2\left[ x{{e}^{x}}-{{e}^{x}} \right]_{-\infty }^{0}=2\,(-1)\,-(0-0)\,]\,=-2\]


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