Prove that the curves y² = 4x and x² = 4y divide the area of the square bounded by x = 0, y = 0, x = 4 and y = 4 into three equal parts.

Given; y² = 4x and x² = 4y

By solving

Area of the region bounded by the curve y=f(x), the x-axis and the ordinates x=a and x=b, where f(x) is a continuous function defined on [a,b], is given by .

Area of middle region

Area of lower region

Area of the upper region

= Area of Square − Area of middle region − Area of lower region

∴ The curves y² = 4x and x² = 4y divide the area of the square bounded by x = 0, y = 0, x = 4 and y = 4 into three equal parts