I am trying to determine the area of this region: $$ M=\{(x,y)\in\mathbb{R}^2:x^2+y^2\leq2, x^4+x^3y^3\leq xy+y^4\} $$
I know that $x^2+y^2\leq2$ represents a disk, but I have no idea of what $x^4+x^3y^3\leq xy+y^4$ represents, which is why I do not know what integration limits to choose (I was thinking of calculating this area with a double integral, but maybe this is not the best approach).
I have found a slightly similar problem on this site: Area enclosed by curve $f(x,y)$ defined implicitly. I have tried to obtain a known function out of $x^4+x^3y^3\leq xy+y^4$ by doing some transformations to the expression (like they do in the problem I have linked), but it has not worked out.
Could anyone give me any tips to approach this problem?
Thank you.