Evaluate $\int\limits_{-1}^{1} \log \left( \frac{2-x}{2+x} \right) \, dx$
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0
Let $f(x) = \log \left( \frac{2-x}{2+x} \right)$
We have, $f(-x) = \log \left( \frac{2+x}{2-x} \right)$
$-\log \left( \frac{2-x}{2+x} \right) = -f(x)$
So, $f(x)$ is an odd function.
$∴\int\limits_{-1}^{1} \log \left( \frac{2-x}{2+x} \right) \, dx = 0$