Integrating a triangle in a 2d plane, bound by $y=4x, x=1$ and $y=0$

Question

I would like to complete the surface integral $\int\int x^2y^2dxdy$ bound by the triangle $y=4x$, $y=0$, $x=1$ integrating over y first. I can do the integral itself, however, I'm unsure of what limits to choose at each stage

Answer 1

If you invert the integral using the Frobenius Theorem you trivially get $$\int_{0}^{1} \int_{0}^{4x} x^2y^2dydx$$