FRQ: Area Between Curves

Let R be the region bounded by the graphs of y = √x, y = 0, and x = 4.

(a) Find the area of region R. (2 points)

(b) Region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a square. Find the volume of the solid. (3 points)

(c) Find the volume of the solid generated when R is revolved about the x-axis. (2 points)

(d) Write, but do not evaluate, an integral expression for the volume of the solid generated when R is revolved about the line y = 3. (2 points)