VOL CROSS-SECTION DISK WASHER

Question

Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves 𝑦=1/x,y=0,x=1,x=3 about the x-axis.

Answer 1

USING THE WASHER METHOD

V = ∫₁³ [π(1/x)²d x = [ -π/x ] |₁³ = - π/3 + π = 2π/3

USING THE SHELL METHOD

V = ∫_1/3¹ 2πy [ 1/y -1 ] d y + ∫₀^1/3 2πy⋅(3-1) d y = 4π/9 + 2π/9 = 6π/9 = 2π/3