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JEE Main20208 Jan 2020Evening ShiftMathematicsArea Under CurvesActual

The area (in sq. units) of the region x ,   y ∈ R 2 : x 2 ≤ y ≤ 3 - 2 x , is.

Options

  1. A32 3
  2. B34 3
  3. C29 3
  4. D31 3

Correct answer

A. 32 3

Step-by-step solution

Point of intersection of y = x 2   &   y = - 2 x + 3 , is obtained by x 2 + 2 x - 3 = 0 ⟹ x = - 3 , 1 . So, area of the required region is ∫ - 3 1 3 - 2 x - x 2   d x = 3 x - x 2 - x 3 3 - 3 1 = 32 3 .

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