The region between the curve y = 2/x and the x-axis from x = 1 to x = 4 is revolved about the x-axis to generate a solid.

a. Find the volume of the solid.

b. Find the center of mass of a thin plate covering the region if the plate’s density at the point (x, y) is δ(x) = √x.

c. Sketch the plate and show the center of mass in your sketch.