Calculating Area of a Piecewise Function
Consider the function defined by: \[f(x) = \begin{cases} x^2, & \text{for } 0 \le x \le 2 \\ 4x – 4, & \text{for } 2 < x \le 4 \end{cases}.\] Calculate the total area between the curve and the x-axis over the interval \[0, 4\].