Evaluate the integral and sketch the region in $x-y$ plane,
$$\int^1_0\int^1_0 x\ \operatorname{max}(x^2,y)\ \mathrm{d}y\ \mathrm{d}x.$$
I have already integrated the equation with when $x^2 > y$ and when $y > x$. Both also have the result of $\frac14$. I just wanna know how do I graph this to show which region is when $x^2$ is larger than $y$ and which region is when $y$ is larger than $x^2$?
After following @lisyarus advice I have concluded this graph Attempt 2