双纽线在四个象限的面积是一样的,所以只需要计算第一象限部分
A = 4∫(0,π/4) (1/2)r^2 dθ
= 4∫(0,π/4) (1/2)4cos2θ dθ
= 8 * (1/2)[sin2θ](0,π/4)
= 4 * sin(π/2)
= 4