The base of a certain solid is a region in the first quadrant bounded by the curve and . Find the volume of the solid if each gross section perpendicular to the x-axis is a square with one edge in the base of the solid.

Attempt to solution:

$\displaystyle A= s^2= (x-x^2)^2$

$\displaystyle V=\int_0^1(x-x^2)^2$

How come the textbook has it the other way round

$\displaystyle V=\int_0^1(x^2-x)^2$