双纽线 $\left(x^{2}+y^{2}\right)^{2}=x^{2}-y^{2}$ 所围成的区域面积可用定积分表示为
A. $2 \int_{0}^{\frac{\pi}{4}} \cos 2 \theta d \theta$
B. $4 \int_{0}^{\frac{\pi}{4}} \cos 2 \theta d \theta$
C. $2 \int_{0}^{\frac{\pi}{4}} \sqrt{\cos 2 \theta} d \theta$
D. $\frac{1}{2} \int_{0}^{\frac{\pi}{4}}(\cos 2 \theta)^{2} d \theta$