# Thread: Find volume of solid using squares

1. ## Find volume of solid using squares

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

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

2. Does it matter? Not in this case.

It is traditional to write things in decreasing exponents.

3. I think what needs to be observed here is that $\displaystyle x-x^2=-\left(x^2-x\right)$ but $\displaystyle \left(x-x^2\right)^2=\left(-\left(x^2-x\right)\right)^2=(-1)^2\left(x^2-x\right)^2=\left(x^2-x\right)^2$