Evaluate $\int_0^4 \lvert x - 2 \rvert\,dx$.

Explanation

1. 01

   $\lvert x - 2 \rvert = 2 - x$ for $x < 2$ and $x - 2$ for $x \ge 2$, so split at $x = 2$.

2. 02

   $\int_0^2 (2 - x)\,dx + \int_2^4 (x - 2)\,dx = 2 + 2 = 4$.