In the figure below, the area bound by the functions  𝑦=1𝑥, 𝑦=4, 𝑥=4 and  is to be revolved around the 𝑥=4 axis. Which of the following methods would be valid in determining the volume of the resulting revolved plane area if the differential strip to be revolved is horizontal?

The method that would be valid in determining the volume of the resulting revolved plane area if the differential strip to be revolved is horizontal is the Disk Method.

Here's why:

1. Identify the shape of the solid: When the area between the curve and the line x=4 is revolved around the line x=4, it forms a solid of revolution.

2. Choose the method: Since the strip is horizontal, we use the Disk Method. The Disk Method involves slicing the region into thin horizontal strips (disks), which are then revolved around the axis of rotation to form thin cylindrical shells.

3. Set up the integral: The volume V of the solid of revolution is given by the integral of π times the square of the radius of the disks times the thickness of the disks. In this case, the radius of each disk is the distance from the curve y=1/x to the line x=4, which is |4-1/x|. The thickness of each disk is a small change