I have: $$ \int_{}^{} \int_{}^{}r\,drd\theta.$$
And I have to find the area bounded by $r=2(2-\sin(\theta))^{1/2}$.
I understand how to find the limits of integration for dr, but how would I find it for (dtheta)? I can't use a graphing calculator for this problem and I'm stuck on what I should do to get the integration limits for dtheta. Is there a way to find them without the graph of the figure?
It's some time ago, but here I go:
I guess you need to find the domain of $\theta$. Which reflects in the question 'What values for $\theta$ are allowed'.
Since the equation doesn't seem to have any problems $\theta \in [0,2\pi]$.
(The equation doesn't have any problems since $2-\sin(\theta)$ is always positive)