Thread: 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 ??

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?

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

Originally Posted by fromTURKEY

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

....how may solutions are there to ?

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..

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

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

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.