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.

Learn how to solve the double integral ∬R (2y - x²) dA by first identifying the region R and setting up the appropriate limits of integration. This guide covers key calculus concepts, including multivariable integration and the use of Fubini's theorem, suitable for undergraduate calculus students.

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