# Thread: Finding the area of a curve

1. ## Finding the area of a curve

How do I find the area of the region in one loop of the curve that has polar equation r^2 = 3 cos^2(theta) - 9 sin^2(theta) ???

2. Polar integration is $\frac{1}{2}\int_{\alpha}^{\beta}[f({\theta})]^{2}d{\theta}=\frac{1}{2}\int_{\alpha}^{\beta}r^{2 }d{\theta}$

You already have r^2.

The area of half a loop in the first quadrant is $\frac{1}{2}\int_{0}^{\frac{\pi}{6}}\left[3cos^{2}{\theta}-9sin^{2}{\theta}\right]d{\theta}$

Integrate and multiply by 2.