Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202519 Apr 2025Evening ShiftMathematicsArea Under CurvesActual

The area enclosed between the curves y ^2=4 x and y =|x| is

Options

  1. A8 3 sq. units
  2. B5 3 sq. units
  3. C4 3 sq. units
  4. 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

Practice Area Under Curves on Quantrex Academy →

More from Area Under Curves

Find the area bounded by the curve y = |2 - x| , the x –axis, and the lines x = 0 and x = 5 2026The area enclosed by the curve y = -x^2 and the line x + y + 2 = 0 is 2026The area of the region bounded by the line y = x + 2 and the curve x = -y^2 is 2026The area of the region in the first quadrant enclosed by the x -axis, the line x = 3 ,y and the circle x^2 + y^2 = 4 is 2026The area of the region bounded by the curve y^2 = x^3 , the y -axis and the lines y = 1 and y = 8 is 2026The area enclosed by the curve x = 3 , y = 3 is 2026The area in square units of the region bounded by the curve y = 16 - x^2 and lines x = 0, x = 4 above the X-axis is 2026The area bounded by the curves y = |x| - 1 and y = -|x| + 1 is 2026 Full Area Under Curves list All MHT CET PYQs