Find the area of the top half of the polar curve : $$r=3-2\cos \theta$$
I'm not sure how to tackle this. I need to find the area of a unique shape (almost a semi-circle), but I don't know where to start.
2026-03-27 23:35:25.1774654525
Find the area of the top half of the polar curve $r=3-2 \cos \theta$
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Draw tha graph of the cartesian equation $y=3-2\cos x$. With this, it is easy to draw (without the need of a computer) the graph in polar coordinates of $r=3-2\cos \theta$, it would look something like that :
Now notice that the top of the figure is obtained when $0\leq \theta \leq \pi$. So, the area is given by $$\frac{1}{2} \int_0^\pi r^2 d\theta = \frac{1}{2} \int_0^\pi (3-2\cos \theta)^2 d\theta$$