Let T be the triangle 1≤x≤2, 0≤y≤3x-3. Find the volume that results by rotating the triangle T around the line x=-1.
using shells,
v = ∫[1,2] 2πrh dx
where r = x+1 and h=y=3x-3
v = 2π∫[1,2] (x+1)(3x-3) dx
= 8π
v = ∫[1,2] 2πrh dx
where r = x+1 and h=y=3x-3
v = 2π∫[1,2] (x+1)(3x-3) dx
= 8π