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JEE Main & Advanced Sample Paper JEE Main Sample Paper-17

  • question_answer
    The area bounded by the curve \[y=f(x),\]the co- ordinate axes and the line \[x=x{{ & }_{1}}\]is given by \[{{x}_{1}}{{e}^{{{x}_{1}}}}.\]Therefore, \[f(x)\]equals

    A) \[{{e}^{x}}\]                                      

    B) \[x{{e}^{x}}+{{e}^{x}}\]

    C) \[x{{e}^{x}}-{{e}^{x}}\]                

    D)  \[x{{e}^{x}}\]

    Correct Answer: B

    Solution :

     \[\int\limits_{0}^{x}{f(x)dx=x{{e}^{x}}}\] \[\Rightarrow \]               \[f(x)=\frac{d}{dx}(x{{e}^{x}})\] \[\Rightarrow \]               \[f(x)=x{{e}^{x}}+{{e}^{x}}\]


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