Final answer:
To find the volume of the solid generated by revolving the region bounded by the graphs of the equations y = x² - 5x and y = 0 about the x-axis, we can use the method of cylindrical shells.
Step-by-step explanation:
To find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis, we can use the method of cylindrical shells.
We need to integrate the volume of each individual shell. The radius of each shell is given by the distance from the x-axis to the curve y = x² - 5x, which is x. The height of each shell is given by the difference between the highest point on the curve and the x-axis, which is y = 0.
Using the formula for the volume of a cylindrical shell, the volume of the solid is given by the integral:
V = ∫ 2πx (x² - 5x) dx