2. Solved Papers
  3. JCECE Engineering

JCECE Engineering JCECE Engineering Solved Paper-2011

  • question_answer
    If\[{{I}_{m}}=\int_{1}^{x}{{{(\log x)}^{m}}dx}\]satisfies the relation \[{{I}_{m}}=K-l{{I}_{m-1}}\],then

    A) \[K=e\]                

    B) \[l=m\]

    C) \[K=\frac{1}{e}\]                             

    D)  None of these

    Correct Answer: B

    Solution :

    \[{{I}_{m}}=\int_{1}^{x}{{{({{\log }_{x}})}^{m}}}dx=[{{(\log x)}^{m}}\cdot x]_{1}^{x}\]                                 \[-\int_{1}^{x}{m{{(\log x)}^{m}}^{-1}\cdot \frac{1}{x}}\cdot x\,\,dx\]                 \[={{(\log x)}^{m}}\cdot x-m\cdot {{I}_{m-1}}\]


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