Does anyone know how to solve x(5-x)^(1/2) about the x axis using the disk method?
May I re-write the question as I understand it?:
Determine the volume when the area, enclosed by the x-axis and the graph of $\displaystyle y = x \cdot \sqrt{5-x}$, rotates about the x-axis.
The volume is composed by cylindrical discs whose radius is y and whose height is dx. The volume of one of these discs is calculated by:
$\displaystyle V_{single\ disc} = \pi \cdot y^2 \cdot dx$
The complete volume of the solid is the sum of all those discs:
$\displaystyle V=\int (\pi \cdot y^2)dx$
Plug in the term of y and determine the borders of the area and you'll get the equation skeeter has posted.