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.

Question

y = 13 sqr.(x)
y = 0, x = 1; about x = −3

Answer 1

the volume of a shell of radius r, height h and thickness dr is

v = 2πrh dr

So, add up your shells, where
r = x+3 = (y/13)^2
h = y

v = ∫[0,2] 2π ((y/13)^2+3) y dy = 2036π/169

Answer 2

oops. the shells have thickness dx.

v = ∫[0,2] 2π (x+2)(13√x)dx = 1644√2/15 π