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JEE Main & Advanced Sample Paper JEE Main Sample Paper-24

  • question_answer
          Let \[f(x)=\int\limits_{0}^{{{x}^{2}}}{\frac{{{t}^{2}}-1}{{{e}^{t}}+1}dt}\] If a is the Point of local maxima and b and \[c(b>c)\] are the points of the local minima, then

    A)  \[a+b+c=1\]               

    B)  \[a+b=c\]

    C)  \[a+c=b\]                    

    D)  \[b+c=a\]

    Correct Answer: D

    Solution :

    \[f'(x)\,=\frac{2x({{x}^{4}}-1)}{{{e}^{{{x}^{2}}}}+1}\]\[x=0=a\] is the point of maxima \[x=\pm \,1\] is the point of minima \[\therefore \,\,b=1\,\,\] and c=-1


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