area enclose between curves
y = |x|, will be y = x in first quadrant, and
x = y2 is a parabola.
Therefore they'll intersect in first quadrant only.
The intersection point is (1,1) as it only satifies y = x and x = y2.
The area inclosed between the curves, will be area under parabola from (0,0) to (1,1) LESS the area of right angled triangle with base as 1 unit and height as 1 unit.
Therefore, the area = [ydx] - (1/2)(1)(1)
= [x dx ] - 1/2 ... note that the limit for integration is 0 to 1, the limit for x.
= [x3/2/(3/2)] - 1/2
= 2/3 - 1/2 = 1/6 sq units.