1. ## Areas of cardioids

How can I determine the bounds of integral which we use while calculating carsioids. For example: find the area shared by r=2(1+sinθ) and r=2 ??

2. Originally Posted by fromTURKEY
HOW CAN I DETERMINE THE BOUNDS OF INTEGRAL WHICH WE USE WHILE CALCULATING CARDIOIDS.FOR EXAMPLE: FIND THE AREA SHARED BY r=2(1+sinθ) and r=2 ??
There is a formula for this you know? Have you tried to graph the two curves to find the bounds for integration?

$2=2\left(1+\sin(\theta)\right)\implies 1+\sin(\theta)=1\implies \sin(\theta)=0$

3. But, is it one of bounds or will we find the bounds after that ?

4. Originally Posted by fromTURKEY
But, is it one of bounds or will we find the bounds after that ?
....how may solutions are there to $\sin\left(\theta\right)=0$?

5. two ! 0 and π. but according to my book, bounds are 0 and π/2
the other bounds are -π/2 and 0 ?? help me please. I have a final exam tomarrow..

6. For the shared area once you have 0 and pi as Drexel pinted out -note from 0 to pi you simply have the area of a half circle and from pi to 2pi you have the area inside the cardioid obtained by doubling the integral of

2(1+sin(t)) from pi to 3pi/2.

See graph in attachment

7. No, I did not understand..How did we determine the bounds as from pi to 3pi/2

8. Ok--- for the area inside the cardioid it should be fairly obvious you could integrate from pi to 2pi.

Now just split that interval in two.