Find the area enclosed between y = x² and y = 2 − x².

Question

G1 Physics · Accepted Answer

The curves intersect where x²=2−x²: 2x²=2 → x=±1. Area = ∫₋₁¹[(2−x²)−x²]dx = ∫₋₁¹(2−2x²)dx = 2[2x−2x³/3]₀¹ = 8/3 square units.