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KEAM Even Functions — practice questions

Explore 1 free Even Functions questions in KEAM Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Even Functions questions and exercises with answers

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$\int_{-1}^{1} \dfrac{x^2}{1+x^2}\,dx$ equals:Read the answer and worked solution →

Worked practice questions

$\int_{-1}^{1} \dfrac{x^2}{1+x^2}\,dx$ equals:

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

Correct answer: B. $(4-\pi)/2$

Integrand $x^2/(1+x^2)$ is **even**, so $I = 2\int_0^1 x^2/(1+x^2)\,dx = 2\int_0^1 [1 - 1/(1+x^2)]\,dx$ $= 2[x - \tan^{-1}x]_0^1 = 2[1 - \pi/4] = (4-\pi)/2$.

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