Fuente TeX:

A(D) = \int_0 ^{ \frac{\pi}{4} } \int_2 ^{ \sqrt{ \frac{12}{ \cos^2(\theta) + 3 \sin ^2 (\theta )} } } \rho \phantom{a} d\rho \phantom{a} d\theta = \int_0 ^{ \frac{\pi}{4} } \frac{\rho ^2}{2} \big|_2  ^{ \sqrt{ \frac{12}{ \cos^2(\theta) + 3 \sin ^2 (\theta )} } } d\theta = \int_0 ^{ \frac{\pi}{4} } \frac{6}{ \cos^2(\theta) + 3 \sin ^2 (\theta )}  - 2 \phantom{a} d\theta