Asked by abneesh
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
x = y − y^2, the y-axis; about y = 1
Answers
Answered by
oobleck
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
v = ∫[0,1] 2πrh dy
where r = 1-y and h = x
v = ∫[0,1] 2π(1-y)(y-y^2) dy