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=x^2# and #y^2=x# rotated about the x-axis?
To use shells, we take our representative slices parallel to the line we are revolving around. So the thickness will be
The height will be the greater
The limits of integration will be
The two curves are:
Solving the first equation for
The second equation already gives
Looking again at our sketch of the region, we see that the curve
The height is
The volume of the representative shell is:
And the limits of the region are
I am sure that you can finish from here.