Volumes by Integration: Shell Method Practice Problem Solution
1. Determine the volume created by rotating the area bounded by the x axis, y=x1/2, x=4 about the x axis.
Here is the volume. Try sketching in the shell.
Now write the equation for the volume, dV, of the shell. Remember:
dV = circumference *height*thickness
dV = 2p r h dy = 2py(4-x)dy
r h dy = 2py(4-x)dy
Now find x in terms of y and substitute that into the equation.
dV = 2p(4-y2)dy Since x=y2
Then set limits and integrate.