How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #y=4-x^2# and #y=0# rotated about the y-axis?
See the explanation, below.
Here is the region with a thin slice taken parallel to the axis of rotation. (To set up for cylindrical shells.)
The volume of a representative shell is
In this case, we have radius