The following definite integral gives the area of the region between the graph of the function f(x) = Icosx - x^2I (I=modulus), the x-asis, and the lines x=-2 and x=2.

the integral of mod cosx - x^2 from -2 to 2.

Describe a different region whose area is given by this integral, and show it on a graph.

how about |x^2-cosx|

or, 2*integral from 0 to 2, since both cosx and x^2 are even?

To find a different region whose area is given by this integral, let's analyze the function f(x) = |cos(x) - x^2| in more detail.

First, let's look at the graph of the function f(x) = |cos(x) - x^2| between -2 and 2:

To graphically represent the function, you can use any graphing tool or software. Alternatively, you can plot a few points and connect them to get a rough idea of the curve.

By analyzing the graph, we can observe that the function |cos(x) - x^2| is symmetric about the x-axis and has a peak around x ≈ -0.739 and x ≈ 0.739. Beyond these points, the function extends indefinitely in both directions.

To find a different region whose area is given by the given integral, we can consider the area between the graph of the function and the x-axis from -2 to some positive value, say x = a, and then double that area.

Thus, the region whose area is given by the integral can be determined by finding the area between the graph of the function f(x) = |cos(x) - x^2| and the x-axis from -2 to some positive value a, and multiplying it by 2.

Now, let's plot the region on a graph:

1. Draw the x-axis and label it accordingly.
2. Choose a positive value, a, for x and mark it on the x-axis.
3. Plot the curve of the function f(x) = |cos(x) - x^2| between -2 and a.
4. Shade the region between the curve and the x-axis from -2 to a.
5. Reflect the shaded region about the x-axis to account for the symmetry of the function.
6. Multiply the area of the shaded region by 2 to get the area of the region between the graph of the function f(x) = |cos(x) - x^2|, the x-axis, and the lines x = -2 and x = 2.

Note: The exact value of a would determine the specific region for which we want to find the area.