Find all points of intersection (r,theta) of the curves r=4cos(theta), r=1sin(theta). Next find the area inclosed in the intersection of the two graphs.

Answer 1

4cosθ = sinθ
16cos^2θ = 1-cos^2θ
17cos^2θ = 1
cosθ = 1/√17

Now use that value of θ (call it Ø) to get the area

A = ∫[0,Ø] 1/2 (sinθ)^2 dθ
+ ∫[Ø,π/2] 1/2 (4cosθ)^2 dθ