Find the area inside the lemniscate r^2=150cos(2theta) and outside the circle r=5sqrt(3).

Question

Please I really need help.

Answer 1

find 0<α<π/4 where the curves intersect

Then, by symmetry,

a = 8∫[0,α] 1/2 (R^2-r^2) dθ
where R=150cos2θ and r=5√3