Q94 / 170 · Manipal (MET) 2015 · Mathematics

$\int_1^4 \log _e[x] d x$ equals

  • A
    $\log _8 2$
  • B
    $\log _\theta 3$
  • Correct answer
    C
    $\log _e 6$
  • D
    None of the above

Solution

Let $I=\int_1^4 \log _\theta[x] d x$ $\begin{aligned} & =\int_1^2 \log _\theta 1 d x+\int_2^3 \log _\theta 2 d x+\int_3^4 \log _\theta 3 d x \\ & =\log _e 2+\log _e 3=\log _e 6\end{aligned}$

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

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