Suppose $$f(x) = \left\lbrace \begin{array}{lll} 2x-8 && \mbox{ if } 0 \leq x \lt 4, \\ 8-2x && \mbox{ if } 4 \leq x \leq 8. \end{array} \right.$$

Evaluate the definite integral by interpreting it in terms of signed area.

$\displaystyle \int_{0}^{8} f(x) \, dx =$

Suggestion: Draw a picture of the region whose signed area is represented by the integral. Then find the signed area using formulas from high school geometry.