The problem asks to evaluate the integral of the function $f(x)$ from $-a$ to $3a$, where $a = 2$. The graph provided shows a semi-circular curve from $-a$ to $a$, followed by a linear segment from $a$ to $3a$.

Step-by-step solution:

1. Identify the segments:

   • From $-a$ to $a$, the curve is a semicircle.
   • From $a$ to $3a$, the curve is a straight line.

2. Semicircular part (from $-a$ to $a$):

   • The curve from $-a$ to $a$ forms a semicircle of radius $a$. The area under this semicircle is $\frac{\pi a^2}{2}$, since the area of a full circle is $\pi r^2$, and a semicircle is half of that.
   • With $a = 2$, the area of the semicircle is: $\text{Area} = \frac{\pi (2)^2}{2} = 2\pi \approx 6.2832$

3. Linear part (from $a$ to $3a$):

   • The line is straight and extends downward with negative slope. The exact equation of the line is not provided, but based on the graph, it looks like it decreases linearly, possibly representing a simple form such as $f(x) = -\frac{f(a)}{2a}(x - a)$ from $a$ to $3a$.
   • This will need more detailed examination from the graph to integrate correctly or find out area or decomposition. the last seems..Concing