the curves intersect where
8-x^2 = x^2
x = ±2
so, using shells,
v = ∫[-2,2] 2πrh dx
where r = 2-x and h = (8-x^2)-x^2
v = 2π∫(2-x)(8-2x^2) dx
= 256π/3
using discs (washers) and symmetry,
v = 2∫[0,2] π(R62-r^2) dy
where R=2+√y and r=2-√y
v = 2π∫[0,2] ((2+√y)^2 - (2-√y)^2) dy
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.
y=8-x^2, y= x^2 ; about x=2
V=?
1 answer
1 answer