How do you find the volume of the region bounded b the line y = x-2, the x-axis, x=2, and x=4 is revolved about the line x = -1?

1 Answer
Oct 18, 2015

V=(52pi)/3

Explanation:

V=pi int_(y_1)^(y_2) (R^2-r^2)dy

y=x-2, x=2 => y_1=2-2=0
y=x-2, x=4 => y_2=4-2=2

x=4 => R=4-(-1)=5
y=x-2 => x=y+2 => r=y+2-(-1)=y+3

V=pi int_(0)^(2) (5^2-(y+3)^2)dy = pi int_(0)^(2) (25-y^2-6y-9)dy

V=pi (16y-3y^2-y^3/3) |_0^2 = pi (32-12-8/3)

V=(52pi)/3