Question

Let r be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when r is revolved about the x-axis: y, y, and x⁰.

Answer 1

The shell method is used to find the volume of a solid generated by revolving a region bounded by curves around an axis.

Step-by-step explanation:

The shell method is used to find the volume of a solid generated by revolving a region bounded by curves around an axis, in this case, the x-axis.

To find the volume using the shell method, we divide the region into infinitesimally thin cylindrical shells and integrate their volumes.

The formula for the volume of a cylindrical shell is V = 2πrhΔx, where r is the distance from the axis to the shell, h is the height of the shell, and Δx is the thickness of the shell.

We integrate the volumes of all the shells to find the total volume of the solid.