Area between curves. I have to calculate area bounded by curves :
$(x^3+y^3)^2=x^2+y^2 $ for $ x,y \ge 0 $.
I tried to use polar coordinates, but I have :
$r^4(\cos^6\alpha +2\sin^3\alpha\cos^3\alpha + \sin^6\alpha)=1$

By your work: $$r=\frac{1}{\sqrt{\sin^3\alpha+\cos^3\alpha}}.$$ Since it's symmetric in respect to $y=x$, we obtain that the needed area it's
$$2\int\limits_0^{\frac{\pi}{4}}d\alpha\int\limits_0^{\frac{1}{\sqrt{\sin^3\alpha+\cos^3\alpha}}}rdr=\int_0^{\frac{\pi}{4}}\frac{1}{\sin^3\alpha+\cos^3\alpha}d\alpha.$$
Can you end it now?
