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
- A1 6
- B1 2
- C1 3
- 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