MHT CET202519 Apr 2025Evening ShiftMathematicsArea Under CurvesActual
The area enclosed between the curves y ^2=4 x and y =|x| is
Options
- A8 3 sq. units
- B5 3 sq. units
- C4 3 sq. units
- D2 3 sq. units
Correct answer
A. 8 3 sq. units
Step-by-step solution
The curves y^2=4x and y=|x| intersect at (0,0) and (4,4) , and their enclosed region lies in the first quadrant. For 0 x 4 , the parabola gives y = 2 x (upper curve) and y = x (lower curve). The area is A = ₀⁴ (2 x - x) , dx = [ 4 3 x^ 3/2 - 1 2 x^2 ]₀⁴ = ( 4 3 (8) - 1 2 (16) ) = 32 3 - 8 = 8 3 . Final answer: 8 3