Use the shell method to find the volume of the solid of revolution generated by revolving the region bounded by the graphs of the given equations about the indicated line.
x = y − y^2, the y-axis; about y = 1
as always, using shells of thickness dy,
v = ∫[0,1] 2πrh dy
where r = 1-y and h = x
v = ∫[0,1] 2π(1-y)(y-y^2) dy