I have this double integral $$I = \int\limits_{}^{} \int\limits_{}^{} y \ dx \cdot dy$$
and I am supposed to calculate it over a triangle with corners at (0,0),(1,2),(-1,1). What I did, was splitting the 3 lines that make the triangle to 3 equations of y = 2x, y = -x, y = (x/2)+3/2, but I am not sure how to set the boundaries for these 3 equations.
Can someone explaine me how to set the boundaries in a double integral please?
Thank you in advance
Guide:
Split the picture into two parts by drawing the line $y=1$.
For $0\le y \le 1$, the boundary on the right is $x=\frac{y}2$ and the boundary on the left is $x=-y$. Hence the lower part of the triangle can be written as $$\int_0^1 \int _{-y}^{\frac{y}{2}} y \, dx\, dy$$
Now I will leave the task of describing the upper part of the triangle to you as an exercise.
As a practice, try to interchange the order of integration, consider how should you split the triangle.