2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Definite Integration

JEE Main & Advanced Mathematics Definite Integration Question Bank Summation of series by Definite Integration, Gamma function, Leibnitz's rule

  • question_answer
    If \[f(x)=\int_{{{x}^{2}}}^{{{x}^{2}}+1}{{{e}^{-{{t}^{2}}}}}dt,\] then \[f(x)\] increases in [IIT Screening 2003]

    A)                 \[(2,\,\,2)\]        

    B)                 No value of \[x\]

    C)                 \[(0,\,\,\infty )\]              

    D)                 \[(-\infty ,\,\,0)\]

    Correct Answer: D

    Solution :

                       \[f'(x)={{e}^{-{{({{x}^{2}}+1)}^{2}}}}.2x-{{e}^{-{{({{x}^{2}})}^{2}}}}.2x=2x{{e}^{-({{x}^{4}}+1+2{{x}^{2}})}}\left( 1-{{e}^{2{{x}^{2}}+1}} \right)\]                 Þ \[f'(x)>0,\forall x\in (-\infty ,0).\]


You need to login to perform this action.
You will be redirected in 3 sec spinner