Final answer:
To find the area of the region bounded by y^2=x and y^2=2−x, you can set up an integral to calculate the area between the two curves.
Step-by-step explanation:
To find the area of the region bounded by y2=x and y2=2−x, you can set up an integral to calculate the area between the two curves.
To calculate this area, you first need to find the points where the two curves intersect by setting y2=x = y2=2−x. Solving this equation gives you two points of intersection (x1, y) and (x2, y).
The area between the curves can then be found by evaluating the definite integral of the difference between the curves, from x1 to x2. The integral would be ∫[(2−x)−x] dx, and the result will give you the area of the region between the curves.