Volume of a solid with known cross sections

[clannad]

Homework Statement

Any cross sectional slice of a certain solid in a plane perpendicular to the x-axis is a square with side AB, with A lying on the curve $$y^2 = 4x$$ and B on the curve $$x^2 = 4y$$. Find the volume of the solid lying between the points of intersection of these two curves.

Homework Equations

$$\int ^{b}_{a} A(x)dx$$

The Attempt at a Solution

I'm not sure if I'm going in the right direction, but so far I've put the curves in terms of y, leaving me with $$y = 2\sqrt{x}$$ and $$y = \frac{x^2}{4}$$. After graphing, I also know that the limits of integration will be from 0 to 4 since the points of intersection are at (0, 0) and (4, 4). From here on, I'm completely lost.

Thanks :)

 

[Russell Berty]

The area of a square is s^2 where s is the length of one side. So, what is the length of one side? The distance from A to B, so find that from your graph (at an arbitrary x value and the expression should be in terms of y.)