Q102 / 180 · COMEDK 2015 · Mathematics

$\int_{1}^{e} \log x d x=$

  • Correct answer
    A
    1
  • B
    $e-1$
  • C
    $e+1$
  • D
    0

Solution

We have, $\int_{1}^{e} \log x d x$ $=\left[\log x \int 1 d x\right]_{1}^{e}-\int_{1}^{e}\left(\frac{d}{d x} \log x \int 1 d x\right) d x$ $=[\log x \cdot x]_{1}^{e}-\int_{1}^{e} \frac{1}{x} \cdot x d x$ $=[e \log e-1 \log (1)]-\int_{1}^{e} 1 d x$ $=e-[x]_{1}^{e}=e-[e-1]=1$

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

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