Final answer:
To find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis, use the method of cylindrical shells and the formula for volume of a solid of revolution. Substitute the given equations and integrate to find the volume.
Step-by-step explanation:
To find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis, we can use the method of cylindrical shells. The formula for the volume of a solid generated by revolving a region about the x-axis is given by:
V = 2π ∫[a, b] x * h(x) dx
In this case, we want to find the volume between the x-values of 3 and 4, so the interval of integration is [3, 4]. The function h(x) represents the height of the cylinder at each x-value, which is the difference between the two equations, y = 8/x and y = 0. The height of the cylinder is given by:
h(x) = (8/x) - 0 = 8/x
Substituting these values into the formula, we have:
V = 2π ∫[3, 4] x * (8/x) dx
Integrating this expression will give us the volume of the solid.