Let

$\displaystyle f(x)=6x(1-x)$ for $\displaystyle 0\leq x\leq 1$

$\displaystyle g(y)=2y$ for $\displaystyle 0 < y < 1$

Calculate $\displaystyle F(w) = \iint_{x^2y \leq w}f(x)g(y)dxdy$ for $\displaystyle 0\leq w\leq 1$

I'm having trouble figuring out what the limits are since w is also a variable.