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JEE Main & Advanced Sample Paper JEE Main Sample Paper-24

  • question_answer
    If \[\int\limits_{0}^{2\pi }{\frac{1}{1+{{\tan }^{4}}x}=\frac{\pi }{k}}\] where \[k\in N\], then k equals

    A)  1                    

    B)  2

    C)  3                                

    D)  4

    Correct Answer: A

    Solution :

    \[I=2\int\limits_{0}^{\pi }{\frac{dx}{1+{{\tan }^{4}}x}=4\int\limits_{0}^{x/2}{\frac{dx}{1+{{\tan }^{4}}x}}}\] Use King \[I=4\int\limits_{0}^{\pi /2}{\frac{dx}{1+{{\cot }^{4}}x}}\] \[\therefore \,\,2I=4\int\limits_{0}^{\pi /2}{dx=4.\frac{\pi }{2}\,\Rightarrow \,I=\pi }\]


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