Solution

Let $f(x) = \begin{cases} x^2 & \text{if } 0 \leq x \leq 2 \\ 2x + 1 & \text{if } 2 < x \leq 4 \end{cases}$. Here $g(x)$ is defined as $g(x) = f(x) + f(4 - x)$. Compute $\int_{0}^{4} g(x)\, dx$.