So, this questioned popped up on a homework in my Calculus II class, and I'm pretty confused. I am familiar with finding the area between two polar curves or two "Cartesian" functions but not a mixture of the two. I've plotted the two functions together so I have a sense of what area I'm trying to find.
The general formula for the area of a polar curve is $\int_a^b\frac12(r)^2d\theta$ where $r(\theta)$ is our function, and $a$ and $b$ are values of $\theta$. If I were tasked with finding the area between two polar curves, I would subtract from the area of the "outer" curve the area of the "inner" curve. I also know that for regular functions of x or y, a similar procedure applies.
But how do I use this here? How do I identify the bounds of integration? And once I do, what do I integrate? I've tried several things and none of it seems to work. Any help wrapping my head around this would be much appreciated.