If $f(x) = \frac{2 - x \cos x}{2 + x \cos x}$ and $g(x) = \ln x$ for $x > 0$,then the value of the integral $\int_{-\pi/4}^{\pi/4} g(f(x)) dx$ is

The value of $\int_{-1}^1 \sin^5 x \cos^4 x \, dx$ is

$\int_0^1 f(1 - x) \, dx$ has the same value as which of the following integrals?

$\int_0^{\frac{\pi}{2}} \frac{300 \sin x+100 \cos x}{\sin x+\cos x} \,dx = \ldots$ (in $\pi$)

$\int_{0}^{a} (a-x)^{\frac{3}{2}} x^{2} dx =$

Let $f:[-1, 2] \rightarrow [0, \infty)$ be a continuous function such that $f(x) = f(1-x)$ for all $x \in [-1, 2]$. Let $R_1 = \int_{-1}^2 x f(x) dx$ and $R_2$ be the area of the region bounded by $y = f(x)$,$x = -1$,$x = 2$,and the $X$-axis. Then $R_2$ is: