Finding the area of a region? I sketched out the graph to get this figure but I can't seem to find the area of the shaded region... would one Y = 4 and the other Y = 8? 
I, in all honesty, am so flabbergasted with this question, any guidance will be much appreciated. I got 28/3 for the first integral (0 to 4) and 292/3 for the second integral (4 to 16)... I feel like I'm doing this wrong.
Okay, I'm going to be honest, can someone please solve this for me? I got 320/3 as my final answer and yet it's still wrong, I'm just about given up at this point, it's literally my last question of this semester.

The area between two curves given by functions $f(x)$ and $g(x)$ is given by,
$$ \int_a^b \vert f(x)-g(x) \vert dx = \int_a^b \textbf{Top Function} - \textbf{Bottom Function }\mathrm{d}x$$
A common mistake students make when trying to compute this is that they don't change the order of the subtraction when the "Top Function" changes from $f(x)$ to $g(x)$. This happens whenever the two curves cross eachother. In your case they seem to cross at $x=4$ so that you need to evaluate an integral from $0$ to $4$ and then another one from $4$ to $16$ always making sure to have to top function come first in the subtraction.
