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 \[f(t)=\int_{\,-t}^{\,t}{\frac{dx}{1+{{x}^{2}}},}\] then \[{f}'(1)\] is                         [Roorkee 2000]

    A)                 Zero      

    B)                 2/3

    C)                 \[-\,1\]

    D)                 1

    Correct Answer: D

    Solution :

                       Given \[f(t)=\int_{-t}^{t}{\frac{dx}{1+{{x}^{2}}}}\] \[=[{{\tan }^{-1}}x]_{-t}^{t}\]\[=2{{\tan }^{-1}}t\]            Differentiating with respect to t, \[{f}'(t)=\frac{2}{1+{{t}^{2}}}\]                                 Þ \[f'(1)=\frac{2}{2}=1\].


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