Final answer:
To find the volume of the solid generated by revolving the region bound by y = 2x, y = 0, and x = 3 about the y-axis using the shell method, integrate the area of each shell.
Step-by-step explanation:
To find the volume of the solid generated by revolving the region bound by y = 2x, y = 0, and x = 3 about the y-axis using the shell method, we need to integrate the area of each shell.
The radius of each shell is given by x, and the height of each shell is given by 2x (the difference between the upper and lower functions). The integral to find the volume is:
V = 2π∫(x)(2x)dx, from 0 to 3
After evaluating the integral, the volume of the solid is 18π cubic units.