Final answer:
To sketch the region of integration, the limits for the inner integral with respect to y are from 0 to √(4−x²) and the limits for the outer integral with respect to x are from -2 to 2. To change the order of integration, reverse the limits and rewrite the integral.
Step-by-step explanation:
To sketch the region of integration, we need to visualize the limits of integration for both x and y. The integral given is ∫²₋₂ ∫₀ √(4−x²) f(x,y) dy dx. The limits for the inner integral with respect to y are from 0 to √(4−x²). The limits for the outer integral with respect to x are from -2 to 2.
To change the order of integration, we need to reverse the limits and rewrite the integral. The new integral will be ∫₀² ∫₀ √(4−x²) f(x,y) dx dy.