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Problem 10 - Entrance Test

Find the area of the region bounded by y = x^2 and y = 2 - x^2.

Correct: A

Intersection points: x^2 = 2 - x^2 => 2x^2 = 2 => x^2 = 1 => x = ±1. Area = ∫[-1,1] (2 - x^2 - x^2) dx = ∫[-1,1] (2 - 2x^2) dx = [2x - (2/3)x^3] from -1 to 1 = (2 - 2/3) - (-2 + 2/3) = 4 - 4/3 = 8/3.