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NTA Abhyas JEE Main2020MathematicsArea Under CurvesPractice

The area bounded by the parabola 4 y = 3 x 2 , the line 2 y = 3 x + 12 and the y -axis is

Options

  1. A10 sq. units
  2. B20 sq. units
  3. C30 sq. units
  4. D36 sq. units

Correct answer

B. 20 sq. units

Step-by-step solution

The intersection point is A 4,12 by solving 2 3 x 2 4 = 3 x + 12 Thus, the required area = ∫ 0 4 3 x + 12 2 - 3 x 2 4 d x = 3 4 x 2 + 6 x - x 3 4 0 4 = 3 4 16 + 24 - 16 = 12 + 8 = 20 sq. units

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