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 $A 4=1$
\[
V=\int_{0}^{5} f(x) d x
\]

Answer

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Answer

Final Answer: The value of the integral is $\boxed{14}$.

Steps

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 $\boxed{14}$.