$\int_{-1 / 2}^{1 / 2} \log \left(\frac{1+x}{1-x}\right) \mathrm{d} x=$

$\int_{-1 / 2}^{1 / 2} \log \left(\frac{1+x}{1-x}\right) \mathrm{d} x=$
  1. $0$
  2. $\frac{1}{2}$
  3. $-1$
  4. $-\frac{1}{2}$

Solution

$\int_{\frac{-1}{2}}^{1 / 2} \log \left(\frac{1+x}{1-x}\right) \mathrm{d} x=0\left[\because \int_{-a}^a f(x) \mathrm{d} x=0\right.$ if $f(x)$ is odd $]$

Asked in: MHT CET 2022 (10 Aug Shift 2)

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