Let for $x \in \mathbb{R}$, $f(x) = \frac{x + |x|}{2}$ and $g(x) = \begin{cases} x, & x < 0 \\ x^2, & x \geq 0 \end{cases}$. Then area bounded by the curve $y = f(g(x))$ and the lines $y = 0$, $2y - x = 15$ is equal to $\underline{\hspace{1cm}}$.
Let for $x \in \mathbb{R}$, $f(x) = \frac{x + |x|}{2}$ and $g(x) = \begin{cases} x, & x < 0 \\ x^2, & x \geq 0 \end{cases}$. Then area bounded by the curve $y = f(g(x))$ and the lines $y = 0$, $2y - x = 15$ is equal to $\underline{\hspace{1cm}}$.