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UPCET / UPSEE Feynman's Trick — practice questions

Explore 1 free Feynman's Trick questions in UPCET / UPSEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Feynman's Trick questions and exercises with answers

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$\displaystyle\int_0^1 \dfrac{x - 1}{\ln x}\, dx = ?$ (Frullani-type)Read the answer and worked solution →

Worked practice questions

$\displaystyle\int_0^1 \dfrac{x - 1}{\ln x}\, dx = ?$ (Frullani-type)

  1. $0$
  2. $\ln 2$
  3. $1$
  4. $e$
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Correct answer: B. $\ln 2$

Use Feynman's trick. Define $I(s) = \int_0^1 (x^s - 1)/\ln x\, dx$. Then $I'(s) = \int_0^1 x^s\, dx = 1/(s+1)$. $I(0) = 0$. **Integrate:** $I(s) = \ln(s+1)$. For our problem, $s = 1$: $I(1) = \ln 2$.

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