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 ??
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