(Solved): Let S be the solid obtained by rotating the region shown in the figure below about the y-axis. The x ...

Let S be the solid obtained by rotating the region shown in the figure below about the y-axis. The x y-coordinate plane is given. There is a curve and a shaded region on the graph. The curve y = 9x(x − 1)2 starts at the origin, goes up and right becoming less steep, changes direction at the approximate point (0.33, 1.33), goes down and right becoming more steep, passes through the approximate point (0.67, 0.67), goes down and right becoming less steep, and ends at x = 1 on the positive x-axis. The shaded region is above the x-axis and below the curve from x = 0 to x = 1. Explain why it is difficult to use the