
Help Me Immediately
I just completed all paractice test except these 2 question.
I try my best but I can not do anything.
Help me, please.
1. Find the area of the region that is enclosed by the rose r = 4cos3Θ
2. Find the area of the region that is inside the circle r = 3sinΘ and outside the cardioids r = 1+sinΘ

2 Attachment(s)
This is a 3 petal rose. To find the limits of integration, we can set
$\displaystyle 4cos(3t)=0$ and find that $\displaystyle t=\frac{\pi}{6}$
This gives the area of half a petal in the first quadrant. So we multiply by 2.
$\displaystyle \int_{0}^{\frac{\pi}{6}}[4cos(3t)]^{2}dt$
For the other one, we can find the region in the first quadrant and multiply by 2:
Where they intersect can be found by $\displaystyle 3sin(t)=1+sin(t)$
As before, $\displaystyle t=\frac{\pi}{6}$
$\displaystyle \int_{\frac{\pi}{6}}^{\frac{\pi}{2}}\left[(3sin(t))^{2}(1+sin(t))^{2}\right]dt$
$\displaystyle \int_{\frac{\pi}{6}}^{\frac{\pi}{2}}\left[4cos(2t)2sin(t)+3\right]dt$