Find the area of the region that lies inside the first curve and outside the second curve. r = 9 cos(θ), r = 4 + cos(θ)

Answer 1

First 2 pre-tasks: find the intersections, and set up the integral. Setting the two equations equal we get

cos θ = 1/2 so θ = ± π/3

In polar coordinates, area is ∫1/2 r²

so here we want the larger area:

1/2 ∫(9cosθ)² dθ

and the smaller area:

1/2 ∫(4+cosθ)² dθ

(both are from -π/3 to π/3)

Then the area is the big area minus the small area

If we're solving these integrals without a calculator we will need the trig identity cos²θ = 1/2 + 1/2cos(2θ)

Does that help?