Q109 / 170 · Manipal (MET) 2021 · Mathematics

$\int_1^e \frac{\log x}{x} d x$ is

  • Correct answer
    A
    $\frac{1}{2}$
  • B
    1
  • C
    $e$
  • D
    None of these

Solution

Let $I=\int_1^e \frac{\log x}{x} d x$ Put $\quad \log x=t \Rightarrow \frac{1}{x} d x=d t$ $\therefore \quad I=\int_0^1 t d t=\left[\frac{t^2}{2}\right]_0^1=\frac{1}{2}$

Hence, the correct answer is option: 'A'.

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