MCQ
$\int_{-1}^1 \log \left(\frac{2-x}{2+x}\right) d x=$
- A2
- B
- C-1
- D1
✓
Answer
(b) : $I=\int_{-1}^1 \log \left(\frac{2-x}{2+x}\right) d x=\int_{-1}^1 f(x) d(x)$
$
f(x)=\log \left(\frac{2-x}{2+x}\right)
$
Now, $f(-x)=\log \left(\frac{2+x}{2-x}\right)=-\log \left(\frac{2-x}{2+x}\right)=-f(x)$
$\therefore f(x)$ is an odd function
$
\therefore \quad \int_{-1}^1 f(x) d x=0
$
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