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

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

If you invert the integral using the Frobenius Theorem you trivially get $$\int_{0}^{1} \int_{0}^{4x} x^2y^2dydx$$
• When $x\in(0,1), y\in$what? And when $y=4x, x=$what? Nov 7, 2021 at 22:52