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Questions  >>  CBSE XII  >>  Math  >>  Integrals
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Q)

Evaluate : $\begin{align*}\int\limits_{-1}^1 log (\frac{2+x}{2-x}) dx \end{align*}$


$(A)\; 0$
$(B)\; 2$
$(C)\; log \;2$
$(D)\; 2\;log\;2$

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A)
$f(x)^{-1} = log (\frac{2+x}{2-x})$
$\begin{align*}f(-x) = log (\frac{2-x}{2+x}) & = log (\frac{2+x}{2-x})^{-1} \\ & = - log (\frac{2+x}{2-x})\end{align*}$
Since $f(-x) = -f(x)$ it is an odd function
$\therefore \begin{align*}\int\limits_{-1}^1 log (\frac{2+x}{2-x}) dx \end{align*} = 0$
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