Question
Use the disk method to find the volume of the solid generated by revolving about the y-axis the region bounded by the curves y=8−x^2 and the curve y=x^2.
Answers
Since the y-axis is also the axis of symmetry for the curves, we can just take one side and revolve it. This will be easiest using shells of thickness dx:
v = ∫[0,2] 2πrh dx
where r=x and h=(8-x^2)-x^2=8-2x^2
v = ∫[0,2] 2πx(8-2x^2) dx = 16π
v = ∫[0,2] 2πrh dx
where r=x and h=(8-x^2)-x^2=8-2x^2
v = ∫[0,2] 2πx(8-2x^2) dx = 16π
Related Questions
Use the disk or the shell method to find the volume of the solid generated by revolving the region b...
So I'm trying to solve this problem but one thing I don't get is, how do I know which method to use...
Find the volume of the solid generated by revolving the region bounded by the given lines and curves...
Find the volume of the solid generated by revolving the region bounded by the given lines and curves...