Calculate the area enclosed by the curves x 2 = 2 - y , x 2 = y

Question

Calculate the area enclosed by the curves x 2 = 2 - y , x 2 = y, 2 3 square units, 4 3 square units, 8 3 square units, 11 3 square units

MARKS App · Accepted Answer

x 2 = 2 - y , x 2 = y Intersection point ⇒ 2 - y = y ⇒ y = 1 ⇒ x = ± 1 A = ∫ - 1 1 [ ( 2 - x 2 ) - ( x 2 ) ] d x = 2 ∫ 0 1 ( 2 - 2 x 2 ) d x = 4 x - x 3 3 0 1 = 8 3 square units.

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