Saturday, June 21, 2025

Volume of a solid in polar coordinates using double integrals

 As in rectangular coordinates, if a solid S is bounded by the surfaces z = f(r, θ) and the surfaces r = a, r = b, θ = ɑ, θ = β, then the volume V of S can be found by integration using the formula:


If the base of the solid can be described as D = {(r, θ), ɑ ≤ θ ≤ β h₁(θ) ≤ θ ≤ h₂(θ)}, the volume V becomes:


Example



Solution

By the method of double integration, the volume is the iterated integral of the form:





No comments:

Post a Comment