∫ 0 2 1 - x 2 d x =

Question

∫ 0 2 1 - x 2 d x =, 1, 2, 3, 1 2

MARKS App · Accepted Answer

1 - x 2 = 1 - x 1 + x = x 2 - 1 x ≥ 1 1 - x 2 - 1 ≤ x 1 x 2 - 1 x - 1 Since ∫ a b f x d x = ∫ a c f x d x + ∫ c b f x d x where a c b ∫ 0 2 1 - x 2 d x = ∫ 0 1 1 - x 2 d x + ∫ 1 2 x 2 - 1 d x = x - x 3 3 0 1 + x 3 3 - x 1 2 = 1 - 1 3 - 0 + 8 3 - 2 - 1 3 - 1 = 2 3 + 2 3 + 2 3 = 6 3 = 2

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