The area of the region enclosed by the lines y = 2x, 2y = x and x = 2 (in sq.units) is...

Step-by-step solution

The given lines are y = 2x , y = x 2 , and x = 2 . The points of intersection of the lines are (0,0) , (2,4) , and (2,1) . The region is bounded by the upper line y = 2x and the lower line y = x 2 from x = 0 to x = 2 . The area of the region is given by the integral of the difference between the upper and lower curves: Area = ₀² (2x - x 2 ) dx Area = ₀² 3x 2 dx Area = [ 3x^2 4 ]₀² Area = 3(2)^2 4 - 0 = 3 Answer: 3