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BITSAT2019MathematicsArea Under CurvesActual

Area bounded by two branches of the curve y - x 2 = x 3 and x = 1 is

Options

  1. A5 4   sq   unit
  2. B3 2   sq   unit
  3. C1 4   sq   unit
  4. D4 5   sq   unit

Correct answer

D. 4 5   sq   unit

Step-by-step solution

Given, curve is y - x 2 = x 3 ⇒   y - x = ± x x ⇒   y = x ± x x ∴ Area bounded = ∫ 0 1 x + x x - x - x x d x = 2 ∫ 0 1 x 3 / 2 d x = 4 5   sq   unit

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