The equation for a parabola is y= x (exp2)

Let us calculate the blue area, as follows

For x=a, the area under the curve and axis x is the integral of xExp 2 between 0 and a, which yields 1/3 a (exp 3)

Let us calculate the grey area,

Due to the symmetry of the two parabolas

We can calculate the area of a rectangle base ( -a to 2a) height a (exp2) which yields 3 a (exp 3) and substract three times the blue area , therefore the grey area is 2 a (exp3)

Then the ratio is 1/3 a (exp3) / 2 a (exp3) = 1/6