# Math Help - Help Me Immediately

1. ## Help Me Immediately

I just completed all paractice test except these 2 question.
I try my best but I can not do anything.

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. This is a 3 petal rose. To find the limits of integration, we can set

$4cos(3t)=0$ and find that $t=\frac{\pi}{6}$

This gives the area of half a petal in the first quadrant. So we multiply by 2.

$\int_{0}^{\frac{\pi}{6}}[4cos(3t)]^{2}dt$

For the other one, we can find the region in the first quadrant and multiply by 2:

Where they intersect can be found by $3sin(t)=1+sin(t)$

As before, $t=\frac{\pi}{6}$

$\int_{\frac{\pi}{6}}^{\frac{\pi}{2}}\left[(3sin(t))^{2}-(1+sin(t))^{2}\right]dt$

$\int_{\frac{\pi}{6}}^{\frac{\pi}{2}}\left[-4cos(2t)-2sin(t)+3\right]dt$