I'm having trouble with the following question:
Find the area of the region inside both of the circles $r = 2a\cos(\theta)$ and $r = 2a\sin(\theta)$, where a is a positive constant.
From what I think i have correct the region is:
$2a\sin(\theta) \le r \le 2a\cos(\theta)$
$0 \le \theta \le \frac{\pi}{4}$
My real question is would it be advantegous to convert this back to cartesian coordinates, or even possible to do that?
I think if I integrate everything according to those functions, I end up with something like
$\int_0^\frac{\pi}{4} \big(\cos(\theta)^2 - \sin(\theta)^2\big) d\theta$
Not exactly the nicest function
Thanks for the help guys! Sorry if I have made any formatting errors, I'm new to the math stackexchange.