Question

How do you find the area of the common interior of `r=3-2sintheta, r=-3+2sintheta`?

Answer 1

The second graph is not real. An attempt to make it, using the Socratic graphics utility ought to fail. Read explanation.

Explanation:

`r =sqrt(x^2+y^2)>= 0`.

This is not possible, from the second equation.

Here, `r = -3+2 sin theta >=0 to sin theta >= 3/2 to theta` is unreal.

Of course, the first gives the limacon in the inserted graph.

graph{x^2+y^2-3sqrt(x^2+y^2)+2y=0 [-12, 12, -6, 6]}