Final answer:
To calculate the volume of the solid formed by rotating the given region around the x-axis, we would use the disk method and set up an integral from x=1 to x=2 using the area of the disks formed.
Step-by-step explanation:
To find the volume V of the solid obtained by rotating the region bounded by y = 4 - \(\frac{1}{2}\)x, y = 0, x = 1, and x = 2; about the x-axis, we use the disk/washer method. We first sketch the region by plotting the lines and points of intersection. Next, we set up an integral from x = 1 to x = 2 with the given functions representing the outer and inner radii of the disks/washers forming the solid. Since there's no inner function (as y = 0 represents the x-axis), it's just a disk method problem. The area of a disk is πr², so the volume integral will be V = π∫(4 - \(\frac{1}{2}\)x)²dx from x = 1 to x = 2.