What is the washer method formula?

For the Washer Method
The area of a disk is the area of a circle. The volume is the area ${\displaystyle \pi r^2}$ times the thickness, which will be either dx or dy depending on the problem. Thus, it will be either ${\displaystyle \pi r^{2}dx}$ or ${\displaystyle \pi r^{2}dy}$
Thus, for some a and b, we'll have ${\displaystyle {\int }_a^b(\pi R^2-\pi r^2)d\text{x or dy}}$
Where R is the radius of the larger disk and r that of the smaller.
The radii functions must have the same independent variable as the differential.
If revolving around a horizontal line ${\displaystyle y=k}$, the thickness of the representative disk will be the differential dx.
In this case:
The larger disk will be determined by the function ${\displaystyle y=g\left(x\right)}$ farther from the line ${\displaystyle y=k}$ and the smaller disk, by the function ${\displaystyle y=f\left(x\right)}$ closer to ${\displaystyle y=k}$
If revolving around a vertical line ${\displaystyle x=h}$, the thickness of the representative disk will be the differential dy.
In this case:
The larger disk will be determined by the function ${\displaystyle x=g\left(y\right)}$ farther from the line ${\displaystyle x=h}$ and the smaller disk, by the function ${\displaystyle x=f\left(y\right)}$ closer to ${\displaystyle x=h}$
It must be taken into account if the graphs of the functions cross each other of the line about which we are rotating.
If a region must be divided into two or more parts, the volume must be calculated using two or more integrals.