find the volume of the solid by using cylindrical shells generated by revolving the,?

Question

functions y= x-x^2 and y=0 about the line x=2

Answer 1

r = 2 - x, dr = -dx
dV = 2πrdrdy
dV = -2π(2 - x)dxdy
..... ..... 0 (x - x^2)
V = -2π∫∫(2-x)dxdy =
..... .... 1 0
..... ..... 0
V = -2π∫(2 - x)(x - x^2)dx
..... .... 1
..... ..... 0
V = -2π∫(2x - 2x^2 -x^2 + x^3)dx
..... .... 1
V = -2π[(x^2 - x^3 + (1/4)x^4)]from x = 1 to x = 0
V = 2π(1 - 1 +(1/4))
V = π/2

Answer 2

2Pi definite integral from 0 to 1 of x(x-x^2) dx

the rest is easy.

Answer 3

assymtote...? shouldnt y=0 sorta be a hint?