To set up the iterated integral for the region $R$ with respect to $f(x, y)$, we need to determine the appropriate limits of integration for $x$ and $y$.

Given:

1. The outer limits of integration are $A = -4$ and $B = 4$ for $x$.
2. The inner limits are functions of $y$, given by $C = 20 - y^2$ and $D = 3$.

This configuration suggests that:

• $x$ ranges from $-4$ to $4$.
• For each fixed $x$ within this range, $y$ is bounded between $y = \sqrt{20 - x^2}$ and $y = 3$.

Thus, the iterated integral for the region $R$ can be set up as follows:

$\iint_R f(x, y) \, dA = \int_{-4}^{4} \int_{3}^{\sqrt{20 - x^2}} f(x, y) \, dy \, dx.$

These bounds represent the limits of integration for $y$ as a function of $x$, allowing us to integrate $f(x, y)$ over the shaded region $R$.

Would you like further clarification or assistance with this setup?

Here are five related questions that might deepen your understanding:

1. How would the limits change if we reversed the order of integration?
2. What geometric shape does the region $R$ represent, based on the bounds given?
3. How do you handle integration when the limits of integration involve functions?
4. What are some techniques for solving integrals over irregular regions?
5. Can this problem be approached with polar coordinates, and how would that change the setup?

Tip: Always sketch the region $R$ when setting up integration limits to visualize the bounds and ensure accuracy.