Suppose that I want to evaluate the following double integral : $$\iint_D(2y-1)$$ where D is a triangle with vertices $(0,1),(1,0),(-1,0)$.
I know the method of constructing the triangle and solving it. My question is since the domain is symmetric can I integrate it over one half and multiply it by 2? I tried it with this problem and the answer was same but I am not sure whether it is mathematically correct? Thank You.