Find the area enclosed by $ρ=1+cos(\theta)$. I can not find the angle of the function to define the limits of the integrals.
This would be the graph of the function:
What I was trying to do, because of the symmetry of the function, was: $$2\int _0^α\int _0^{1+cos\left(\theta \right)}\:ρ\:dρd\theta$$
However, I can't correctly find the angle $α$. I would highly appreciate any suggestions.
$\alpha$ is the angle at which $r=1+\cos(\theta) =0$, therefore $$ A= 2\int _0^\pi \int _0^{1+\cos\left(\theta \right)}\:r\:\mathrm dr\mathrm d\theta$$