Final answer:
The volume of the solid generated by revolving the given curve about the x-axis from x=1 to infinity is infinite.
Step-by-step explanation:
The volume of the solid generated by revolving the region under the curve y = x/3 from x = 1 to x = ∞ (infinity) about the x-axis is calculated using the method of disks or washers. This involves an integral that for this function and limits becomes improper due to the infinity range.
To find this volume, we employ the formula for the volume of a solid of revolution using integration:
V = π * ∫R(x)2 dx, where R(x) is the function y = x/3 and the integral is evaluated from 1 to infinity.
Calculation step:
V = π * ∫_1∞ (x/3)2 dx
V = (π/9) * ∫_1∞ x2 dx
Upon solving the improper integral, we conclude that the volume is infinite, as the area under the curve approaches infinity.