Final answer:
The area enclosed by the curves y=x²-9 and y=9-x² is 54 square units.
Step-by-step explanation:
The area enclosed by the curves y=x²-9 and y=9-x² is equal to the area of the region between the two curves. To find this area, we need to find the points where the curves intersect and integrate between those points.
To find the points of intersection, set the two equations equal to each other: x²-9=9-x². Simplifying, we get 2x²=18, and solving for x, we get x=3 or x=-3.
Now, we integrate the difference between the two equations from x=-3 to x=3: ∫(9-x²) - (x²-9) dx. Simplifying and integrating, we get the enclosed area to be 54 square units.