Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET20192 May 2019Morning ShiftMathematicsArea Under CurvesActual

The area of the region bounded by the curve y = 2 x - x 2 and the line y = x is ________ square units.

Options

  1. A1 6
  2. B1 2
  3. C1 3
  4. D7 6

Correct answer

A. 1 6

Step-by-step solution

Given curves y = 2 x - x 2 and y = x y = x y = 2 x - x 2 Points of intersection of curve y = 2 x - x 2 and y = x is x = 0 , and x = 1 Hence, required area = ∫ 0 1 y 1 - y 2 d x ∫ 0 1 2 x - x 2 - x d x x 2 2 - x 3 3 0 1 = 1 6 sq. unit

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