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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
The value of $\int_1^e \log x d x$ is
  • A
    $0$
  • ✓
    $1$
  • C
    $e$
  • D
    $e \log e$
✓

Answer

Correct option: B.
$1$
Let $I=\int_1^e \log x d x$
Using integration by parts, we get $I=[x \log x]_1^e-\int_1^e \frac{1}{x} \cdot x d x$
$I=[x \log x]_1^e-[x]_1^e=e \log e-\log 1-e+1$
$=e-0-e+1=1 \quad[\because \log e=1 \text { and } \log 1=0]$

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