We have two equations
1.y=|x|^3
2.x=y^3
Now there two points of intersection between these two curves .
Put the value of y form equation 1 into 2
x=|x|^6=x^6
Or,x^5*(1-x)=0
Or, x=0 or 1
Hence the two points are (0,0),(1,1)
Area enclosed by the curves
=Integration from 0 to 1 of ( x^(1/3)-x^3)dx
=4/3-1/4
=13/12