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MHT CET202620 April 2026Morning ShiftMathematicsArea Under CurvesActual

The area of the region lying in the first quadrant and bounded by the curve y = 4x^2 , the Y-axis, and the lines y = 2 , y = 4 is...

Options

  1. A1 3 [8 + 2 2 ] sq. units
  2. B1 3 [8 - 2 2 ] sq. units
  3. C1 2 [8 - 2 2 ] sq. units
  4. D1 2 [8 + 2 2 ] sq. units

Correct answer

B. 1 3 [8 - 2 2 ] sq. units

Step-by-step solution

The given curve is y = 4x^2 . In the first quadrant, x = y 2 . The required area is bounded by the curve, the Y-axis, and the lines y = 2 and y = 4 . Area = ₂⁴ x , dy Area = ₂⁴ y 2 , dy Area = 1 2 [ y^ 3/2 3/2 ]₂⁴ Area = 1 3 [ 4^ 3/2 - 2^ 3/2 ] Area = 1 3 [ 8 - 2 2 ] sq. units. Answer: 1 3 [8 - 2 2 ] sq. units

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