Question

find the area inside the cardioid r=1-sin theta and outside the circle r=1/2

Answer 1

you just want an answer?

Answer 2

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

Answer 3

i wanted to c how to do it

Answer 4

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

Answer 5

i am exploiting the symmetry

Answer 6

it is best to sketch the region for these problems

Answer 7

sorry that 1 should be 1/2

Answer 8

and one of your limits should be pi/6

Answer 9

well

Answer 10

what is the lower limit then?

Answer 11

its pi/6

Answer 12

what is you upper limit then?

Answer 13

5pi/6

Answer 14

are you looking at the graph of the region?

Answer 15

if you use those limits you will capture the wrong area

Answer 16

hey i figured it out ty

Answer 17

cool

Answer 18

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

Answer 19

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