Calc help! Area of region bound by curve/limacons - please help quiz tomorrow!?

Question

I have a quiz on this stuff but I was in the hospital getting my appendix out during this lesson. These are the sample problems my professor gave me to look out to help prepare me but my books are in my dorm and I can't find this stuff online anywhere! Please help!!!!!!

1.) Find the area of the region bounded by the given curve:
r= e^theta
on the interval:
(6/3)pi is less or equal to Theta is less or equal to 2pi

2.)Find the area of the region bounded by:
r = 8 - 5sintheta

3.) Find the area of the region inside:
r = 9sintheta
but outside:
r = 4

4.) Find the area of the region bounded by:
r = 10cos2theta

5.) Find the area of the region bounded by:
r^2 = 72cos2theta

6.) Find the area inside the loop of the following limacon:
r = 10 - 20sintheta

7.) Find the area of the region outside:
r = 5 + 5sintheta
but inside:
r = 15sintheta

Thanks! Any help on how any of these are done would be awesome!!!

Answer 1

For the area of limaçons go to
1) I don´t understand the intervall of t as 6pi/3=2pi
3) A = 1/2Int (9sin t-4)^2dt
9sint >4 sin t >4/9 so 0.4606<=t<=2.6810
Google search "area of Pascals limaçon" Wolfram