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I see the image you uploaded contains a mathematical problem. However, to assist you better, I will need to extract the relevant mathematical details. Let me analyze the content of the image to help you with the solution.The image shows a mathematical expression with the following details:

- There's a function involving an integral of a piecewise-defined function.
- The problem involves a graph that defines the behavior of a function, and the limits for the integration are labeled as \( x = 0 \) and \( x = 4 \).
- Below, the result of the definite integral seems to be connected to the area under the curve, represented visually in the graph.

To solve this problem effectively, I need to confirm if you're working on finding the integral or interpreting the graph. Could you clarify the specific goal of this problem, such as whether you're looking for the value of the integral or understanding the graph's properties?

Feel free to let me know, and I'll dive into the solution!

Also, would you like further details on:

1. How to approach solving integrals of piecewise functions?
2. Interpretation of area under the curve in integrals?
3. The geometric meaning of definite integrals?
4. Calculating areas using integral results?
5. How to interpret piecewise function graphs in calculus?

**Tip**: Always check the units when dealing with integrals in physics or engineering problems, as they can affect the final interpretation!

Calculate the integral of a piecewise function defined by a graph, with the definite integral over the interval from x = 0 to x = 4.

Explore the process of calculating the definite integral of a piecewise function over the interval from x = 0 to x = 4. This problem involves interpreting the graph, applying integral calculus, and understanding the area under the curve. Suitable for students in Grades 11-12.

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