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