The volume of a solid of revolution using the method of shells involves slicing the solid perpendicular to the x-axis and rotating the slice to form a cylindrical shell. To calculate the volume of one shell, the formula 2πxf(x)dx is used, where f(x) is the height of the shell and x is the radius of rotation.
The question involves finding the volume of a solid of revolution, which requires calculus techniques. To set up the problem for the method of shells, we imagine slicing the solid perpendicular to the x-axis and then rotating this slice about the x-axis. We then represent this slice as a cylindrical shell with certain dimensions. Since the problem refers to graphs of x-1 and √x_2, we need to clarify these functions as this seems to be a typo.
Assuming we are working with functions x-1 and √x, the volume of one such cylindrical shell with a height of f(x) and radius x when rotated about the x-axis is given by the formula 2πxf(x)dx, where f(x) is the function representing the outer boundary of the solid.
The actual integration to find the total volume of the solid would require the limits of integration, which are the points where the two functions intersect, and the integration of the shell volume formula across those limits. The final answer would be obtained after performing this definite integral.