Finding Area Between Polar Curves - Help Understanding Bounding

[itzela]

I am having trouble finding the area between 2 polar curves... I have the procedure down, but the bounds are throwing me off. Any help with understanding how to bound would be great appreciated!

I have attatched one problem that I am having hard time with and the work I have done. I know that I am doing something wrong because I am getting a negative number for an area (which shouldn't be).

 

[lurflurf]

You can't write that as one integral in that way. The Functions do not respond to the parameters the same way, different bounds are needed for each.
$$\frac{A}{2}=\frac{1}{2}\int_{\frac{\pi}{3}}^{\pi}(1+\cos(\theta))^2 d\theta - \frac{1}{2}\int_{\frac{\pi}{3}}^{\frac{\pi}{2}}(3\cos(\theta))^2 d\theta$$

 

[itzela]

Thanks
After working on it for a little while i arrived at the same expression... and i was a little unsure about it, but you confirmed it!