Three regions are defined in the figure.
The x y coordinate plane is given. A rectangle containing a line, a curve, and three shaded regions is on the graph.
The rectangle is formed by the origin, point A (1, 0), point B (1, 4), and point C (0, 4).
The line y = 4x begins at the origin, goes up and right, and ends at point B (1, 4).
The curve y = 4∜x begins at the origin, goes up and right becoming less steep, and ends at point B (1, 4).
Region R1 is below the line, above the x-axis and left of the line segment A B.
Region R2 is above the curve, right of the y-axis and below the line segment B C.
Region R3 is below the curve and above the line.
Find the volume generated by rotating the given region about the specified line.
ℛ3 about O C