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Question
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Solution
\[Let\ I = \int_{- 1}^1 \log\frac{2 - x}{2 + x} d x\]
\[Here\ f\left( x \right) = \log\left( \frac{2 - x}{2 + x} \right)\]
\[f\left( - x \right) = \log\left( \frac{2 + x}{2 - x} \right)\]
\[ = - \log\left( \frac{2 - x}{2 + x} \right)\]
\[ = - f\left( x \right)\]
\[\text{Hence} f\left( x \right) \text{is an odd function}, \]
Therefore,
\[I = 0\]
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