Find the area bounded by the curve $x^4+y^4=x^2+y^2$ I am stuck with this problem which deals with evaluating an Area
The problem reads :

Find the area bounded by the curve $x^4+y^4=x^2+y^2$.

I tried factorizing the expression and expressing $y$ in terms of $x$, not able to proceed with that idea. Someone please help me out.

Expressing the curve in polar coordinates, we have\begin{align}x^4+y^4=x^2+y^2&\iff\rho^4\cos^4\theta+\rho^4\sin^4\theta=\rho^2\\&\iff\rho=\frac1{\sqrt{\cos^4\theta+\sin^4\theta}}.\end{align}Hence, the area that you're after is\begin{align}\int_0^{2\pi}\int_0^{1/\sqrt{\cos^4\theta+\sin^4\theta}}\rho\,\mathrm d\rho\,\mathrm d\theta&=\int_0^{2\pi}\frac2{3+\cos(4\theta)}\,\mathrm d\theta\\&=\pi\sqrt2.\end{align}
