To solve the double integral $\iint_R (2y - x^2) \, dA$, we need to know the region $R$ over which we are integrating. Could you specify the limits or describe the region $R$ so we can proceed with the calculation?

Once you provide the limits or a description of the region, I can guide you through the solution. Would you like details on how to approach double integrals in general or this specific type?

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Here are 5 related questions that could help deepen understanding:

1. How are the limits of integration chosen in a double integral?
2. What is the geometric interpretation of a double integral?
3. How does changing the order of integration affect the result of a double integral?
4. What techniques are used to solve double integrals over irregular regions?
5. How would this integral change if we were to switch to polar coordinates?

Tip: Always visualize the region of integration, especially for double integrals, to understand the limits better.