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Problem 10 - Entrance Test

Find the area between y = x^2 and y = 2x - x^2.

Correct: A

Intersection: x^2 = 2x - x^2 ⇒ 2x^2 - 2x = 0 ⇒ x=0,1. Area = ∫0^1 (2x - x^2 - x^2) dx = ∫0^1 (2x - 2x^2) dx = [x^2 - 2x^3/3]_0^1 = 1 - 2/3 = 1/3.