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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 43

  • question_answer
    If \[f(x)=\left\{ \begin{matrix}    \sqrt{\left\{ x \right\}} & for & x\in /Z  \\    1 & for & x\in /Z  \\ \end{matrix} \right.\]where \[\{.\}\]denotes the fractional part of x, then the area bounded by \[f(x)\]and \[g(x)\] for \[x\in \left[ 0,6 \right]\]is

    A) \[\frac{2}{3}\]              

    B)        \[2\]           

    C) \[\frac{10}{3}\]                     

    D)       \[6\]

    Correct Answer: B

    Solution :

    [b] \[f(x)\] and \[g(x)\] are periodic with period 1. \[\therefore \]  Required area \[=\int\limits_{0}^{6}{\left[ f\left( x \right)-g\left( x \right) \right]}dx=6\int\limits_{0}^{1}{\left( \sqrt{x}-{{x}^{2}} \right)}\,dx=2\]


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