Final answer:
To find the volume of the solid obtained by rotating the region bounded by the curves y=0 and y=x(2−x) about the axis x=0, use the method of cylindrical shells.
Step-by-step explanation:
To find the volume of the solid obtained by rotating the region bounded by the curves y=0 and y=x(2−x) about the axis x=0, we can use the method of cylindrical shells.
The volume of the solid can be calculated by integrating the area of each cylindrical shell. The height of each shell will be the difference between the two curves, which is given by y=x(2−x), and the radius of each shell will be the x-coordinate at that point. Thus, the integral we need to evaluate is:
V = ∫[0,2] 2πx(x(2−x)) dx
Simplifying and evaluating the integral gives the volume of the solid.