Question

Find by double integration the area lying inside the cardioid r= a(1 + cos O) and outside the circle r= a.​

Answer 1

Answer:

attempting to solve this problem, I reasoned that the area inside the cardioid but outside the circle is the area of the cardioid minus the area of the circle. This gave me the setup:

12(∫2π0(1+cos(θ))2−cos2(θ) dθ)=12(∫2π01+2cos(θ)+cos2(θ)−cos2(θ) dθ)=12(∫2π01+2cos(2θ) dθ)=12(θ+sin(2θ))|2π0=π