Final answer:
To find the area enclosed between the curves y=x^2 and y=2-x^2, we need to find the points of intersection between the two curves and evaluate the areas under the curves separately in the intervals -1≤x≤1 and 1≤x≤2.
Step-by-step explanation:
To find the area enclosed between the curves y=x2 and y=2-x2, we need to find the points of intersection between the two curves. Setting the two equations equal to each other, we get: x2=2-x2. Simplifying, we get: 2x2=2. Solving for x, we find x=±1.
Since the curves intersect at x=±1, we need to evaluate the areas under the curves separately in the intervals -1≤x≤1 and 1≤x≤2.
For -1≤x≤1, the area under the curve y=2-x2 is greater than the area under the curve y=x2. Therefore, the area between the curves in this interval is given by the integral: ∫(2-x2 - x2) dx, for x ranging from -1 to 1.