To set up a definite integral that yields the area of the region shown, we need to integrate the function $f(x) = 4 - |x|$ over the interval that covers the shaded region.

From the graph, we observe that the shaded region is symmetric around the y-axis, extending from $x = -2$ to $x = 2$. Therefore, the integral to find the area is:

$\int_{-2}^{2} (4 - |x|) \, dx$

This integral will give the total area under the curve of $f(x) = 4 - |x|$ from $x = -2$ to $x = 2$.

Would you like further details on setting up this integral or have any questions?

Related Questions

1. How would you evaluate this integral to find the exact area?
2. What effect does the absolute value have on the integration process?
3. How can you split the integral to avoid the absolute value?
4. What are some other ways to calculate areas under symmetric curves?
5. How does symmetry affect the limits of integration in such problems?

Tip

When dealing with functions involving absolute values, consider breaking the integral into sections where the function behaves as a simple linear expression without the absolute value.