2. Solved Papers
  3. JAMIA MILLIA ISLAMIA

JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2012

  • question_answer
        \[\int{\frac{dx}{\sqrt{{{e}^{2x}}-1}}}\]equals to

    A)  \[{{\sin }^{-1}}({{e}^{x}})+C\]   

    B)  \[{{\cos }^{-1}}({{e}^{x}})+C\]

    C)  \[{{\sec }^{-1}}({{e}^{x}})+C\]  

    D)  \[{{\tan }^{-1}}({{e}^{x}})+C\]

    Correct Answer: C

    Solution :

                    \[f(x)={{e}^{x}}g(x)\] On differentiating with respect to\[x,\]we get \[f(x)={{e}^{x}}g(x)+{{e}^{x}}g(x)\] At\[x=0\]                 \[f(0)={{e}^{0}}g(0)+{{e}^{0}}g(0)\] \[\Rightarrow \]               \[f(0)=g(0)+g(0)\]                                 \[=1+2\] \[\Rightarrow \]               \[f(0)=3\]


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