Find the area of the region that lies inside the first curve and outside the second curve. r = 5 − 5 sin(𝜃), r = 5

Answer 1

First, set the curves equal to each other to find the points of intersection:

5 - 5sin(θ) = 5

sin(θ) = 0

θ = π, 2π [you may need a graphing utility to see this]

This is the general formula for the area enclosed between two polar curves:

r₁ ​= 5 − 5sin(θ) (outer curve)

r₂ = 5 (inner curve)

Bounds are θ₁ = π and θ₂ = 2π

From here, use a calculator to find the approximate value, which should be 69.635.

Hope this was helpful. Credits to Roger R. for catching my error with the bounds of integration.