If f(x)=
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. (1) $\log _{\mathrm{e}} 3$

2. (2) $\log _{\mathrm{e}} \mathrm{e}$

3. (3) $\log _{\mathrm{e}} 2$

4. (4) $\log _{\mathrm{e}} 1$

Correct Option: , 4

Solution:

$g(f(x))=\log \left(\frac{2-x \cos x}{2+x \cos x}\right), x>0$