Avolcano fills the volume between the graphs z=0 and z=1/(x^2+y^2)^10 and outside the cylinder x+y=1. find the volume.

For this case, we use the cylindrical coordinates: 
x² + y² = r² 
dV = r dz dr dθ 

The limits are:
z = 0 to z = 1/(r²)^10 = 1/r^20
r = 1 to ∞ 
θ = 0 to 2π 

Integrating over the limits:
V = ∫ [0 to 2π] ∫ [1 to ∞] ∫ [0 to 1/r^20] r dz dr dθ 
V = ∫ [0 to 2π] ∫ [1 to ∞] rz | [z = 0 to 1/r^20] dr dθ 
V = ∫ [0 to 2π] ∫ [1 to ∞] 1/r^19 dr dθ 
V = ∫ [0 to 2π] −1/(18r^18) |[1 to ∞] dθ 
V = ∫ [0 to 2π] 1/18 dθ 
V = θ/18 |[0 to 2π] 
V = π/9

show da graph

step-by-step explanation: