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UPCET / UPSEE Power Reduction — practice questions

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

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Power Reduction questions and exercises with answers

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$\displaystyle\int_0^{\pi/2} \sin^2 x\, dx = ?$Read the answer and worked solution →

Worked practice questions

$\displaystyle\int_0^{\pi/2} \sin^2 x\, dx = ?$

  1. $\pi/4$
  2. $\pi/2$
  3. $1$
  4. $\pi^2/8$
Show answer and solution

Correct answer: A. $\pi/4$

$\sin^2 x = (1 - \cos 2x)/2$. $\int_0^{\pi/2} (1 - \cos 2x)/2\, dx = \tfrac{1}{2}[x - \tfrac{1}{2}\sin 2x]_0^{\pi/2} = \tfrac{1}{2}(\pi/2 - 0) = \pi/4$.

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