Mathematics Question from JEE Main 2023 · 31 January, Shift 1

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