The integral given in the image is:

$\int \int \frac{x^2}{4a \cdot 2\sqrt{a^2}} \, dy \, dx$

The instruction also suggests "by changing the order of integration." To proceed, we need to understand the region of integration (the limits for $x$ and $y$) so we can swap the order of integration accurately. However, the limits are not visible in the provided image.

Would you be able to clarify or provide additional information about the limits of integration? This will help in changing the order of integration correctly.

Do you have any specific questions on this? Here are five follow-up questions related to this topic:

1. What are the general conditions for changing the order of integration?
2. How does the region of integration affect the process of changing the order?
3. What methods can simplify double integrals before changing the order?
4. When would changing the order of integration simplify the problem?
5. What is the interpretation of this integral in a physical context?

Tip: When changing the order of integration, carefully analyze the region of integration boundaries; this is essential for setting the correct new limits.