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UPCET / UPSEE Symmetry Cancellation — practice questions

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

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Symmetry Cancellation questions and exercises with answers

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$\displaystyle\int_0^{\infty} \dfrac{\ln x}{1 + x^2}\, dx = ?$Read the answer and worked solution →

Worked practice questions

$\displaystyle\int_0^{\infty} \dfrac{\ln x}{1 + x^2}\, dx = ?$

  1. Diverges
  2. $0$
  3. $\pi/4 \cdot \ln 2$
  4. $\ln(\pi/2)$
Show answer and solution

Correct answer: B. $0$

Split at $x = 1$ and substitute $x = 1/u$ in the part from $1$ to $\infty$: $\int_1^\infty \ln x/(1+x^2)\,dx = \int_0^1 -\ln u/(1+u^2)\,du$. **So total = $\int_0^1 \ln x/(1+x^2)dx + \int_0^1 -\ln u/(1+u^2)du = 0$.**

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