Area of first and second curves of polar graphs!!!

Question

Find the area of the region that lies inside the first curve and outside the second curve.

r² = 2cos(2θ)

r = 1

Answer 1

If you plot the polar curve, you will see that you can use symmetry, taking the area in the first quadrant and multiplying by four.

The two curves intersect when 2cos(2θ) = 1 or θ=π/6

A = 4∫₀^π/6 (1/2)2cos(2θ)dθ = 4sin(2θ)/2 |₀^π/6 = 2(sin(π/3) - sin(0))

= 2(√3/2) = √3