Question

${\int }_{-1}^{1}log\frac{2-x}{2+x}dx=$ [Roorkee 1986; Kurukshetra CEE 1998]

• A. 2
• B. 1
• C. -1

Answer 1

$Letf\left(x\right)=log\left(\frac{2-x}{2+x}\right)$
$\Rightarrow f(-x)=log{\left(\frac{2-x}{2+x}\right)}^{-1}=-log\left(\frac{2-x}{2+x}\right)=-f\left(x\right)$
$\therefore {\int }_{-1}^{1}log\left(\frac{2-x}{2+x}\right)dx=0$