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JEE Main201912 Jan 2019Morning ShiftMathematicsArea Under CurvesActual

The area (in sq. units) of the region bounded by the parabola, y = x 2 + 2 and the lines, y = x + 1 , x = 0 and x = 3 , is

Options

  1. A17 4
  2. B21 2
  3. C15 2
  4. D15 4

Correct answer

C. 15 2

Step-by-step solution

Area of region A B C D A = ∫ 0 3 x 2 + 2 - x + 1 d x = ∫ 0 3 x 2 - x + 1 d x = x 3 3 - x 2 2 + x 0 3 = 27 3 - 9 2 + 3 = 12 - 9 2 = 15 2

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