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

  • question_answer
    \[\int{\frac{1}{f(x)}dx=\log {{(f(x))}^{2}}+C}\], then\[f(x)\]is

    A) \[x+\alpha \]               

    B) \[2x+\alpha \]

    C) \[\frac{x}{2}+\alpha \]                      

    D) \[{{x}^{2}}+\alpha \]

    Correct Answer: C

    Solution :

     Differentiating w.r.t\[.x,\] we get \[\frac{1}{f(x)}=\frac{1}{{{(f(x))}^{2}}}2f(x)f'(x)\] \[\Rightarrow \]\[f'(x)=\frac{1}{2}\Rightarrow f(x)=\frac{1}{2}x+C\]where \[C\] is a constant.


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