Suppose that R is the finite region bounded by y =x , y=x + 2, x = 0, and x = 4.Find the exact value of the volume of the object we obtain when rotating R about the x -axis.

Answer 1

f(x) = x

g(x) = x+2

V = π∫⁴₀ (g(x))²-(f(x))² dx = π∫⁴₀ x²+4x+4-x² dx = π[2x²+4x]⁴₀ = π[32+16 -0 -0] = 48π