Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the labeled regions are $A 1=8, A 2=4, A 3=1$ and $A 4=1$ \[ V=\int_{0}^{5} f(x) d x \]

Step 1 ：The integral of a function over an interval can be interpreted as the area under the curve of the function over that interval.

Step 2 ：In this case, the areas of the regions under the curve are given as: \(A1 = 8\), \(A2 = 4\), \(A3 = 1\), and \(A4 = 1\).

Step 3 ：We can simply add up these areas to find the value of the integral: \(V = A1 + A2 + A3 + A4\).

Step 4 ：Substituting the given values, we get: \(V = 8 + 4 + 1 + 1\).

Step 5 ：Calculating the above expression, we find that \(V = 14\).

Step 6 ：Final Answer: The value of the integral is \(\boxed{14}\).