## anonymous 5 years ago find the area inside the cardioid r=1-sin theta and outside the circle r=1/2

1. anonymous

2. anonymous

I would definitely exploit the symmetry so you only have one definite integral

3. anonymous

i wanted to c how to do it

4. anonymous

the integral you want is$\int^{\frac{3\pi}{2}}_{\frac{5\pi}{6}}\left[\left[1-\sin\theta\right]^2-1^2\right]d\theta$

5. anonymous

i am exploiting the symmetry

6. anonymous

it is best to sketch the region for these problems

7. anonymous

sorry that 1 should be 1/2

8. anonymous

and one of your limits should be pi/6

9. anonymous

well

10. anonymous

what is the lower limit then?

11. anonymous

its pi/6

12. anonymous

what is you upper limit then?

13. anonymous

5pi/6

14. anonymous

are you looking at the graph of the region?

15. anonymous

if you use those limits you will capture the wrong area

16. anonymous

hey i figured it out ty

17. anonymous

cool

18. anonymous

those are tricky, the iterated integrals in multi-variable are even more awesome

19. anonymous

yah. oh do you think you can help me with graphing a problem u can see the problem if u click on this link http://www.twiddla.com/511680