Question

Find the total area of the shaded region.

Answer 1

The two curves intersect when
`y=0` and
`y=1`. Over the range
`0\le y\le1`, the curve
`x=12y^2` lies above
`x=12y^3`. Hence the area of the shaded region is

`\displaystyle \int_0^1 (12y^2 - 12y^3) \, dy = 4y^3 - 3y^4\bigg|_0^1 = (4-3)-(0-0) = \boxed{1}`