Final answer:
The question asks for the volume of the solid generated by revolving region r about the x-axis using the shell method. To find the volume using the shell method, we need to integrate the formula for the volume of a cylindrical shell. We first need to find the equations of the curves that bound the region r and express the variables in terms of x.
Step-by-step explanation:
The question asks for the volume of the solid generated when the region r is revolved about the x-axis using the shell method. To find the volume using the shell method, we need to integrate the formula for the volume of a cylindrical shell. The formula for the volume of a cylindrical shell is:
V = 2πrh
where r is the distance from the axis of rotation to the edge of the shell, and h is the height of the shell. In this case, we need to express r and h in terms of x. To do this, we need to find the equations of the curves that bound the region r. Once we have the equations, we can set up the definite integral to find the volume.