Solve the following systems of equations:

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 integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} g(f(x)) d x$ is :

  1. $\log _{\mathrm{e}} 3

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

  3. $\log _{\mathrm{e}} \mathrm{e}$

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


Correct Option: , 4

Solution:

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