Using the shell method to compute the volume of a solid of revolution, we start with defining the various variables and function needed. Let's denote:
- `x` as the variable of interest.
- `f(x)` as the function whose graph defines the region that we are revolving.
- `a` and `b` as the bounds of the region on the x-axis.
- `c` as the line about which we are revolving the region.
The volume `V` of the solid that we form by this process is given by the integral:
```
2 * pi * ∫[a, b] (x * f(x) * |x - c| dx)
```
The integral here represents the sum of all the infinitesimally thin cylindrical shells in the solid of revolution. Each shell has a radius of `|x - c|` (the distance between the x-coordinate and the line of revolution), a height of `f(x)` (the value of the function at that x-coordinate), and a thickness of `dx`. We multiply this by `x`, the distance from the origin to the shell, because that's what gives the shell its circular shape when we revolve it around the origin line.
We then multiply everything by `2 * pi`, which is the circumference of a circle with radius 1. This effectively adds up all the circumferences of the cylindrical shells to give us the total volume.
Given specific values for `a`, `b`, `c`, and `f(x)`, we would be able to compute the value of the integral and get a numerical answer for the volume.
Currently, the problem statement provides no definite values for `a`, `b`, `c`, and `f(x)`. From the standpoint of the task, we need these values or some additional conditions to correctly find the volume of the solid of revolution.