Find the area contained between {y }^(2) = x and y = {x}^(2)

Question

Find the area contained between


`{y }^(2) = x`
and

`y = {x}^(2)`

Answer 1

The area is given by

`\displaystyle\int_0^1\sqrt x-x^2\,\mathrm dx=\frac23x^(3/2)-\frac13x^3\bigg|_(x=0)^(x=1)`

so the area is

`\frac23-\frac13=\frac13`