JEE Main & Advanced Sample Paper JEE Main Sample Paper-38

  • question_answer 85) The value of\[\int\limits_{-\pi /4}^{\pi /4}{(x|x+{{\sin }^{3}}x+x{{\tan }^{2}}x+1)dx}\]is

    A) \[0\]                             

    B) \[1\]

    C) \[\pi /4\]                                   

    D) \[\pi /2\]

    Correct Answer: D

    Solution :

    \[I=\int\limits_{\pi /4}^{\pi /4}{{}}(\underset{\begin{smallmatrix}  \downarrow  \\  odd\,\,f \end{smallmatrix}}{\mathop{x|x|}}\,+\underset{\begin{smallmatrix}  \downarrow  \\  odd\,\,f \end{smallmatrix}}{\mathop{{{\sin }^{3}}x}}\,+x\underset{\begin{smallmatrix}  \downarrow  \\  odd\,\,f \end{smallmatrix}}{\mathop{{{\tan }^{2}}x}}\,+1)dx\] \[I=\int\limits_{-\pi /4}^{\pi /4}{dx}=\frac{\pi }{2}\] \[[\because \,\,\int\limits_{-a}^{a}{f(x)}dx=0,\] as\[f(x)\]is an odd function]

adversite



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