I'm suppose to calculate the area bounded by the curve
$(x^2+y^2)^2 = a(x^3-3xy^2)$
and my guess was to convert this equation into polar coordinate (x=rcos$\theta$, y=rsin$\theta$ and $r^2=x^2+y^2$). On doing so I obtained the equation,
$r^4 = a r^3 (cos^3\theta -3cos\theta sin^2\theta)$
now if I double integrate the equation I should get the area bounded by the curve. This is the part where I can't help myself. How do we find the boundaries?
I plot the graph, and got a flower like figure with 3 petals and from there I know $0 \leq r \leq a$ but I can't figure out what is the boundaries of $\theta$. Is there a step-by-step method to calculate the boundaries?
Thanks.
