I have the following exercise and I can't understand how to infer the inequalities to solve the double integral.
How do I know if x is simply between 2 and 14 (according to the points) or if I have to use the given equations?
"Let $d(x,y)$ be the density - in $g/cm^2$ - of a thin plate at point $(x, y)$, being the plate of shape of a region $R$. We can show that the mass $M$ - in g - of this plate is given by $M = \int \int_{R}{d(x,y) dA}$.
Consider a plate of density $d(x,y) = 4y$ in the shape of a triangle with vertices $A(2,4)$, $B(6,8)$ and $C(14,4)$. Knowing that the equations of lines $AB$, $BC$ and $AC$ are, respectively, $x - y + 2 = 0$, $x + 2y - 22 = 0$ and $y - 4 = 0$, we can conclude that the mass of this plate in grams is:"
