posted by Anonymous .
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations y = 0.5x^2, y = 2, and x = 0 about the line y = 2.
v = ∫ πr^2 dx
v = ∫[0,2] π(2-x^2/2)^2 dx
v = ∫ 2πrh dy
where r=2-y and h=x
v = ∫[0,2] 2π(2-y)√(2y) dy
How do you know the r is 2-y and not just y?
Because it is rotated about the line y = 2 ,
not y = 0 , which would have been the x-axis