Final answer:
To calculate the volume V of the solid of revolution about the x-axis, integrate the area of circular disks between x = 4 and x = 8. Assuming y = ln(x) is the upper bound function, apply the disk/washer method, where the volume is the integral of π times the radius squared, representing each disk's area.
Step-by-step explanation:
To find the volume V of the solid obtained by rotating the region bounded by the curves x = 4, x = 8, y = 0, and y = In(4)X about the x-axis, one can utilize the method of cylindrical shells or the disk/washer method depending on the function's orientation. In this case, it seems there is some confusion in the expression for the upper bound; however, assuming y = In(4)X is the natural logarithm function (possibly written as ln(x)), the disk or washer method would be suitable. Applying this method, the volume is calculated by integrating the area of circular disks formed by slices perpendicular to the axis of rotation — in this case, the x-axis. The formula for volume in terms of the cross-sectional area A and height h is V = Ah, and for a rotated solid, the area would be the area of each disk, which is πr².
The exact integral set up to find the volume would be dependent on the correct interpretation of the upper function. Without the exact, correct formulas, remember the main concept — that the volume of a solid of revolution can be found by integrating the area of the cross-sections along the axis of rotation.