Question

${\int }_{\frac{\pi }{2}}^{-\frac{\pi }{2}}ln\left(\frac{2-sinx}{2+sinx}\right)dx=$ ___

• A. $-\pi log2$
  
• B. $-\frac{\pi }{2}log2$
  
• C. $\frac{\pi }{2}log2$
  
• D. $0$

Answer 1

The correct option is D $0$

$f\left(x\right)=log\left(\frac{2-sinx}{2+sinx}\right)$ is an odd function
$\therefore {\int }_{\frac{\pi }{2}}^{-\frac{\pi }{2}}f\left(x\right)dx=0$