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Indian Navy AA (Artificer Apprentice) Integration by Parts — practice questions

Explore 1 free Integration by Parts questions in Indian Navy AA (Artificer Apprentice) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Integration by Parts questions and exercises with answers

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$\int_1^2 \dfrac{\log x}{x^2}\,dx$ equals:Read the answer and worked solution →

Worked practice questions

$\int_1^2 \dfrac{\log x}{x^2}\,dx$ equals:

  1. $(1 - \log 2)/2$
  2. $\log 2 - 1$
  3. $1 + \log 2$
  4. $\log 2/2$
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Correct answer: A. $(1 - \log 2)/2$

Integration by parts with $u = \log x$, $dv = dx/x^2$ gives $v = -1/x$: $[-\log x/x]_1^2 + \int_1^2 dx/x^2 = (-\log 2/2 - 0) + [-1/x]_1^2 = -\log 2/2 + (1 - 1/2) = (1 - \log 2)/2$.

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