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JEE Main & Advanced Sample Paper JEE Main Sample Paper-14

  • question_answer
    Let \[\int\limits_{0}^{1}{{{e}^{{{x}^{2}}}}dx=k,}\] the sum of all possible values of [k], where \[[\cdot ]\] denotes the greatest integer function

    A)  1                                            

    B)  2                 

    C)  3                                            

    D)  4

    Correct Answer: A

    Solution :

     We have, \[0<x<1\] \[\Rightarrow \]               \[0<{{x}^{2}}<x<1\] \[\Rightarrow \]               \[{{e}^{{{x}^{2}}}}<{{e}^{x}}\] \[\Rightarrow \]               \[\int_{0}^{1}{{{e}^{{{x}^{2}}}}dx<\,\int_{0}^{1}{{{e}^{x}}dx=e-1}}\] \[\Rightarrow \]               \[k<e-1\] \[\Rightarrow \]               \[[k]=1\]


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