Question: If $f(x)=\frac{2-x \cos x}{2+x \cos x}$ and $g(x)=\log _{e} x,(x>0)$ then the
value of the integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} g(f(x)) d x$ is :
(1) $\log _{\mathrm{e}} 3$
(2) $\log _{\mathrm{e}} \mathrm{e}$
(3) $\log _{\mathrm{e}} 2$
(4) $\log _{\mathrm{e}} 1$
Correct Option: , 4
Solution:
$g(f(x))=\log \left(\frac{2-x \cos x}{2+x \cos x}\right), x>0$
