∫y = 2x-x？ The intersection with the X axis is (0,0), (2,0), ∴y=2x-x? The area enclosed by the X axis is s = ∫ (0,2) (2x-x? )dx=4/3 .

Again, y=mx, y=2x-x? The intersection of is (0,0), (2m, 2m-m? ), ∴y=mx and y=2x-x? Closed area s1= ∫ (0,2-m) (2x-x? -mx)dx=S/2=2/3 .

And, ∫ (0,2-m) (2x-x? -mx)dx=(2-m)？ /6,∴(2-m)？ /6=2/3,m=2-2^(2/3)。

For reference.