Find the area of the region inside the polar curve r = 2 - 2 sin θ and outside the polar curve r = 3.

Question

Find the area of the region inside the polar curve r = 2 - 2 sin θ and outside the polar curve r = 3. Your work must include the integral, but you may use your calculator to find the area to 3 decimal places

Answer 1

intersection points: 3 = 2 - 2sinθ, sinθ = - 1/2, θ = 7π/6 or θ = 11π/6.

So area A = 1/2∫_7π/6^11π/6[(2 - 2sinθ)² - 3²]dθ = 1/2∫_7π/6^11π/6(4sin²θ - 8sinθ - 5)dθ = 4.6526

I use TI-84 to evaluate integral